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<h1 class="title toc-ignore">Regularized Gaussian Derivatives: Correlated Null N(0, 1) Z Scores</h1>
<h4 class="author"><em>Lei Sun</em></h4>
<h4 class="date"><em>2017-05-09</em></h4>
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<p><strong>Last updated:</strong> 2018-05-15</p>
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<div id="introduction" class="section level2">
<h2>Introduction</h2>
<p>We are using a regularization term on <span class="math inline">\(w\)</span> which is</p>
<p><span class="math display">\[
\sum\limits_{l = 1}^L\lambda_l\left|w_l\right| \ ,
\]</span> where</p>
<p><span class="math display">\[
\lambda_l =
\begin{cases}
0 & l \text{ is odd;} \\
\lambda / \rho^{l/2}, \ \ \ \ \lambda >0, \ \rho\in\left(0, 1\right) & l \text{ is even.}
\end{cases}
\]</span></p>
<p>This regularization is meant to tackle multiple issues at once, including to restrict the number of Gaussian derivatives, to prevent overfitting, to stop the algorithm going crazy and unstable, and to generate non-negative empirical densities of the correlated null.</p>
<p>We are not regularizing the odd order coefficients <a href="mosek_reg_3.html#regularizing_even_orders_only">because</a> they are generally small but non-negligible. Furthermore, unlike the even order ones, we don’t have a clear idea how <span class="math inline">\(\text{var}\left(W_l^s\right) = \bar{\rho_{ij}^l}\)</span> roughly decays with respect to <span class="math inline">\(l\)</span>.</p>
<p>There are three tuning parameters in this regularization scheme, <span class="math inline">\(L\)</span>, the highest order of Gaussian derivative to fit, <span class="math inline">\(\lambda\)</span>, a general (global) regularization parameter, and <span class="math inline">\(\rho\)</span>, a specific (local) shrinkage parameter to control the decaying rate of <span class="math inline">\(w_l\)</span>. We are setting <span class="math inline">\(L = 10\)</span> and <span class="math inline">\(\rho = 0.5\)</span>, and try different choices of <span class="math inline">\(\lambda\)</span>.</p>
<pre class="r"><code>L = 10
rho = 0.5</code></pre>
<p>We are using four different kinds of data sets of correlated nulls simulated from the real GTEx/Liver data. The first, called “typical,” are <a href="gaussian_derivatives_2.html">data sets well studied and documented</a> for being fitted by Gaussian derivatives. The second, called “hostile,” are data sets that are very unfriendly to both <code>BH</code>’s FDR-controlling procedure and <code>ASH</code> in terms of its estimated <span class="math inline">\(\hat\pi_0\)</span>. The third, called “friendly,” on the contrary, are data sets that are very friendly to both <code>BH</code> and <code>ASH</code>, whose empirical distributions are yet not necessarily close to <span class="math inline">\(N\left(0, 1\right)\)</span>. Finally, the fourth, called “iid,” are independent random <span class="math inline">\(N\left(0, 1\right)\)</span> samples.</p>
<p>The hope is for all four data sets, this regularization scheme could automatically reach a variety of goals and give a sufficiently good fit.</p>
</div>
<div id="typical" class="section level2">
<h2>Typical</h2>
<p>The results of these data sets can be compared with previous documentation with known optimal Gaussian derivative orders, such as <a href="gaussian_derivatives_2.html">here</a>, <a href="mosek_reg.html#correlated_null7">here</a>, and <a href="mosek_reg_2.html#correlated_null">here</a>.</p>
<div id="no-regularization-lambda-0" class="section level3">
<h3>No regularization: <span class="math inline">\(\lambda = 0\)</span></h3>
<pre class="r"><code>CorNullPlot("typical", L, lambda = 0, rho)</code></pre>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 3
pihat0 estimated by ASH: 0.184423
Unnormalized w:
0 : 1 ; 1 : -0.0358645746922219 ; 2 : 0.196863594846729 ; 3 : 0.00997486072754378 ; 4 : -0.0244265081565814 ; 5 : 0.000298521020828936 ; 6 : -0.00289686959704202 ; 7 : 0.000227258831584183 ; 8 : -0.000684282416825896 ; 9 : -8.21789726780818e-06 ; 10 : -3.3953875566361e-05 ;
Normalized w:
0 : 1 ; 1 : -0.0358645746922219 ; 2 : 0.278407165769766 ; 3 : 0.0244333190378092 ; 4 : -0.119664962363111 ; 5 : 0.00327013393994956 ; 6 : -0.0777311680912606 ; 7 : 0.0161337765487923 ; 8 : -0.137402818804405 ; 9 : -0.00495042202521986 ; 10 : -0.064680127772705 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-6-1.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 489
Number of False Discoveries by ASH at lfsr = 0.05: 1446
pihat0 estimated by ASH: 0.1522796
Unnormalized w:
0 : 1 ; 1 : 0.0345501445384415 ; 2 : 0.733251674198138 ; 3 : -0.151188207900136 ; 4 : 0.185424312479517 ; 5 : -0.0533305072968751 ; 6 : 0.0211293095698867 ; 7 : -0.00647923650278792 ; 8 : 0.000823585128891623 ; 9 : -0.00028582227222612 ; 10 : -2.52784009252051e-05 ;
Normalized w:
0 : 1 ; 1 : 0.0345501445384415 ; 2 : 1.03697446228378 ; 3 : -0.370333964481153 ; 4 : 0.908389902962399 ; 5 : -0.584206436993847 ; 6 : 0.566958870190842 ; 7 : -0.459980161008776 ; 8 : 0.165374581389968 ; 9 : -0.172177970302609 ; 10 : -0.0481538609204241 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-6-2.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 639
Number of False Discoveries by ASH at lfsr = 0.05: 2300
pihat0 estimated by ASH: 0.04750946
Unnormalized w:
0 : 1 ; 1 : 0.0227244539615043 ; 2 : 0.92101434792072 ; 3 : 0.0222103145256307 ; 4 : 0.175694879344268 ; 5 : -0.0134165085467778 ; 6 : 0.00392982154182872 ; 7 : -0.00480255115990118 ; 8 : -0.000586133715906366 ; 9 : -0.000291508028046953 ; 10 : 2.65975448800262e-06 ;
Normalized w:
0 : 1 ; 1 : 0.0227244539615043 ; 2 : 1.30251098196969 ; 3 : 0.0544039376145207 ; 4 : 0.860725609626624 ; 5 : -0.146970487480621 ; 6 : 0.105448177283665 ; 7 : -0.340947309892716 ; 8 : -0.117694716072657 ; 9 : -0.175603042426075 ; 10 : 0.00506667522509486 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-6-3.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 1
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 0.9998824
Unnormalized w:
0 : 1 ; 1 : 948001617.513726 ; 2 : -1852913923.39639 ; 3 : 2388146729.0879 ; 4 : -1942466863.08905 ; 5 : 1219931877.00972 ; 6 : -554762623.066314 ; 7 : 190275605.485957 ; 8 : -51698609.2012088 ; 9 : 8514828.56300786 ; 10 : -1308353.32230037 ;
Normalized w:
0 : 1 ; 1 : 948001617.513726 ; 2 : -2620416000.37712 ; 3 : 5849740917.16201 ; 4 : -9516105313.66569 ; 5 : 13363684153.1569 ; 6 : -14885843238.6285 ; 7 : 13508227953.9901 ; 8 : -10380998339.054 ; 9 : 5129292017.85067 ; 10 : -2492335812.82459 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-6-4.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 1
Number of False Discoveries by ASH at lfsr = 0.05: 357
pihat0 estimated by ASH: 0.07619716
Unnormalized w:
0 : 1 ; 1 : 0.00386042091758454 ; 2 : 0.395233653180317 ; 3 : -0.0177592602991958 ; 4 : 0.0191478560140696 ; 5 : -0.00364437632299771 ; 6 : -0.00288104662639495 ; 7 : -0.000337256191165567 ; 8 : -0.000212164374593046 ; 9 : -4.66643453550456e-05 ; 10 : 1.37192624335069e-06 ;
Normalized w:
0 : 1 ; 1 : 0.00386042091758454 ; 2 : 0.558944792633868 ; 3 : -0.0435011259422965 ; 4 : 0.0938049538055052 ; 5 : -0.0399221424028716 ; 6 : -0.0773065932355867 ; 7 : -0.0239428144113575 ; 8 : -0.0426022683063849 ; 9 : -0.0281103785445223 ; 10 : 0.00261343847306088 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-6-5.png" width="672" style="display: block; margin: auto;" /></p>
</div>
<div id="lambda-1" class="section level3">
<h3><span class="math inline">\(\lambda = 1\)</span></h3>
<pre class="r"><code>CorNullPlot("typical", L, lambda = 1, rho)</code></pre>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 3
pihat0 estimated by ASH: 0.184423
Unnormalized w:
0 : 1 ; 1 : -0.0360764946561849 ; 2 : 0.198386768132035 ; 3 : 0.00901395541835672 ; 4 : -0.0201370500252101 ; 5 : -0.000550122547300102 ; 6 : -0.000243659125003317 ; 7 : -1.92186474132937e-05 ; 8 : -0.000125953061368301 ; 9 : -2.93811804138163e-05 ; 10 : 1.51034667667792e-10 ;
Normalized w:
0 : 1 ; 1 : -0.0360764946561849 ; 2 : 0.28056125808769 ; 3 : 0.0220795913391696 ; 4 : -0.0986509949733276 ; 5 : -0.00602629057096938 ; 6 : -0.00653806040214643 ; 7 : -0.00136438861704368 ; 8 : -0.0252911739999481 ; 9 : -0.0176990826129307 ; 10 : 2.87712122398752e-07 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-7-1.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 489
Number of False Discoveries by ASH at lfsr = 0.05: 1446
pihat0 estimated by ASH: 0.1522796
Unnormalized w:
0 : 1 ; 1 : 0.0382720564222799 ; 2 : 0.723957047593695 ; 3 : -0.141261297887049 ; 4 : 0.17378916477765 ; 5 : -0.0472968968741243 ; 6 : 0.0173650746067691 ; 7 : -0.00532305271510779 ; 8 : 0.000511710551126635 ; 9 : -0.000219072768393111 ; 10 : -2.31826988482601e-05 ;
Normalized w:
0 : 1 ; 1 : 0.0382720564222799 ; 2 : 1.02382987528259 ; 3 : -0.346018100226566 ; 4 : 0.851389553059418 ; 5 : -0.518111546359069 ; 6 : 0.465953847061092 ; 7 : -0.377899254626673 ; 8 : 0.10275066318801 ; 9 : -0.131968388316005 ; 10 : -0.0441616722276958 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-7-2.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 639
Number of False Discoveries by ASH at lfsr = 0.05: 2300
pihat0 estimated by ASH: 0.04750946
Unnormalized w:
0 : 1 ; 1 : 0.0223556913438548 ; 2 : 0.916740955025879 ; 3 : 0.0218891094396244 ; 4 : 0.172881230445589 ; 5 : -0.0134617737282905 ; 6 : 0.00376825719933721 ; 7 : -0.00480328049020991 ; 8 : -0.000564405807267297 ; 9 : -0.000291745094113606 ; 10 : 8.09167312092846e-10 ;
Normalized w:
0 : 1 ; 1 : 0.0223556913438548 ; 2 : 1.29646749178046 ; 3 : 0.0536171490510185 ; 4 : 0.846941601392408 ; 5 : -0.147466342700302 ; 6 : 0.101112951053052 ; 7 : -0.340999087208252 ; 8 : -0.113331786644218 ; 9 : -0.175745849891238 ; 10 : 1.54141594332499e-06 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-7-3.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 1
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 0.9998824
Unnormalized w:
0 : 1 ; 1 : 18.0701102380429 ; 2 : -36.0134906763067 ; 3 : 45.1561454250037 ; 4 : -37.2608396643896 ; 5 : 23.0978908836177 ; 6 : -10.5550014881213 ; 7 : 3.62691359800924 ; 8 : -0.968975075928181 ; 9 : 0.164546200480334 ; 10 : -0.0232098025643446 ;
Normalized w:
0 : 1 ; 1 : 18.0701102380429 ; 2 : -50.9307669428299 ; 3 : 110.609515042172 ; 4 : -182.540089130822 ; 5 : 253.024717355007 ; 6 : -283.220409960608 ; 7 : 257.485322546778 ; 8 : -194.568651056863 ; 9 : 99.1218444911693 ; 10 : -44.2133032061989 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-7-4.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 1
Number of False Discoveries by ASH at lfsr = 0.05: 357
pihat0 estimated by ASH: 0.07619716
Unnormalized w:
0 : 1 ; 1 : 0.00370167318278368 ; 2 : 0.39411523441055 ; 3 : -0.0180828275775568 ; 4 : 0.0194176203907137 ; 5 : -0.00375358465692172 ; 6 : -0.00227753645456231 ; 7 : -0.00032592434598118 ; 8 : -0.000130598234701831 ; 9 : -4.35362529225419e-05 ; 10 : 3.57929373928491e-09 ;
Normalized w:
0 : 1 ; 1 : 0.00370167318278368 ; 2 : 0.557363109641251 ; 3 : -0.0442937006717421 ; 4 : 0.0951265239526212 ; 5 : -0.0411184597620263 ; 6 : -0.0611127160036223 ; 7 : -0.0231383332089507 ; 8 : -0.0262239174026249 ; 9 : -0.0262260306182651 ; 10 : 6.81834319444681e-06 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-7-5.png" width="672" style="display: block; margin: auto;" /></p>
</div>
<div id="lambda-10" class="section level3">
<h3><span class="math inline">\(\lambda = 10\)</span></h3>
<pre class="r"><code>CorNullPlot("typical", L, lambda = 10, rho)</code></pre>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 3
pihat0 estimated by ASH: 0.184423
Unnormalized w:
0 : 1 ; 1 : -0.0360231032814232 ; 2 : 0.198004631503733 ; 3 : 0.00848396367266838 ; 4 : -0.0192673173429187 ; 5 : -0.000913693546826654 ; 6 : -6.98930940597347e-10 ; 7 : -0.00013786898239914 ; 8 : -1.4550127334419e-09 ; 9 : -4.03039794052092e-05 ; 10 : 3.16144550026949e-11 ;
Normalized w:
0 : 1 ; 1 : -0.0360231032814232 ; 2 : 0.280020835285267 ; 3 : 0.0207813819943463 ; 4 : -0.0943901924048558 ; 5 : -0.0100090113248772 ; 6 : -1.87542851370424e-08 ; 7 : -0.00978772679385683 ; 8 : -2.92164238120541e-07 ; 9 : -0.0242789245045857 ; 10 : 6.02236697558202e-08 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-8-1.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 489
Number of False Discoveries by ASH at lfsr = 0.05: 1446
pihat0 estimated by ASH: 0.1522796
Unnormalized w:
0 : 1 ; 1 : 0.0504759960297731 ; 2 : 0.686491721129383 ; 3 : -0.111934208775094 ; 4 : 0.133707257997524 ; 5 : -0.0309742814883289 ; 6 : 0.00706330717764512 ; 7 : -0.00238881538932786 ; 8 : 1.14874587282051e-10 ; 9 : -5.83139706773415e-05 ; 10 : -3.37001119646057e-11 ;
Normalized w:
0 : 1 ; 1 : 0.0504759960297731 ; 2 : 0.970845902478022 ; 3 : -0.274181696261143 ; 4 : 0.655029114001198 ; 5 : -0.339306253473448 ; 6 : 0.18952841994212 ; 7 : -0.169589069164318 ; 8 : 2.3066634058438e-08 ; 9 : -0.0351280571430325 ; 10 : -6.41967230976329e-08 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-8-2.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 639
Number of False Discoveries by ASH at lfsr = 0.05: 2300
pihat0 estimated by ASH: 0.04750946
Unnormalized w:
0 : 1 ; 1 : 0.0194979034611927 ; 2 : 0.881399833370166 ; 3 : 0.0202952891320483 ; 4 : 0.149606345019525 ; 5 : -0.0125010098851659 ; 6 : 0.00328865844826621 ; 7 : -0.00441151119171934 ; 8 : -7.86344085887155e-05 ; 9 : -0.000263759546136583 ; 10 : 4.02706012758681e-11 ;
Normalized w:
0 : 1 ; 1 : 0.0194979034611927 ; 2 : 1.24648759822547 ; 3 : 0.0497131025557711 ; 4 : 0.732918415161216 ; 5 : -0.136941702114008 ; 6 : 0.0882439661412266 ; 7 : -0.313186226090982 ; 8 : -0.0157896639303183 ; 9 : -0.15888748958586 ; 10 : 7.6713117208551e-08 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-8-3.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 1
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 0.9998824
Unnormalized w:
0 : 1 ; 1 : 0.157079819472207 ; 2 : -0.176247923530239 ; 3 : 0.259270042791677 ; 4 : -0.0303625113757191 ; 5 : 0.127659806187516 ; 6 : -0.00915615359204601 ; 7 : 0.0223863800659267 ; 8 : -6.59829790247414e-10 ; 9 : 0.00116297535962442 ; 10 : 1.6560385410784e-05 ;
Normalized w:
0 : 1 ; 1 : 0.157079819472207 ; 2 : -0.24925220379656 ; 3 : 0.635079310429168 ; 4 : -0.148745320359923 ; 5 : 1.3984431107128 ; 6 : -0.245685382130925 ; 7 : 1.58927532629776 ; 8 : -1.3249277035593e-07 ; 9 : 0.700570796574129 ; 10 : 0.031546556216868 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-8-4.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 1
Number of False Discoveries by ASH at lfsr = 0.05: 357
pihat0 estimated by ASH: 0.07619716
Unnormalized w:
0 : 1 ; 1 : 0.0037421572469342 ; 2 : 0.388630237002326 ; 3 : -0.0184459635481736 ; 4 : 0.0207870740897271 ; 5 : -0.0037246892167014 ; 6 : -0.000505318351905671 ; 7 : -0.00023837133681814 ; 8 : 1.80694742300713e-10 ; 9 : -3.21365453502741e-05 ; 10 : 8.51227164805379e-12 ;
Normalized w:
0 : 1 ; 1 : 0.0037421572469342 ; 2 : 0.54960615191696 ; 3 : -0.0451831985070036 ; 4 : 0.101835449530521 ; 5 : -0.0408019260736721 ; 6 : -0.0135591142216709 ; 7 : -0.0169226861594427 ; 8 : 3.62832162930918e-08 ; 9 : -0.0193589012775412 ; 10 : 1.62153747885429e-08 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-8-5.png" width="672" style="display: block; margin: auto;" /></p>
</div>
<div id="lambda-100" class="section level3">
<h3><span class="math inline">\(\lambda = 100\)</span></h3>
<pre class="r"><code>CorNullPlot("typical", L, lambda = 100, rho)</code></pre>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 3
pihat0 estimated by ASH: 0.184423
Unnormalized w:
0 : 1 ; 1 : -0.0339029123785526 ; 2 : 0.191348166480557 ; 3 : 0.0110728235529016 ; 4 : -0.00672709448200233 ; 5 : 0.000170545146738018 ; 6 : 1.6210790987194e-10 ; 7 : -2.57099814035759e-05 ; 8 : -3.73974432587683e-12 ; 9 : -4.34050545775016e-05 ; 10 : 9.55207011029823e-14 ;
Normalized w:
0 : 1 ; 1 : -0.0339029123785526 ; 2 : 0.270607172172028 ; 3 : 0.0271227677164805 ; 4 : -0.0329558978647961 ; 5 : 0.00186822847882882 ; 6 : 4.3498116739688e-09 ; 7 : -0.00182522761446675 ; 8 : -7.50934700860504e-10 ; 9 : -0.0261469973624583 ; 10 : 1.81961294527458e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-9-1.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 489
Number of False Discoveries by ASH at lfsr = 0.05: 1446
pihat0 estimated by ASH: 0.1522796
Unnormalized w:
0 : 1 ; 1 : 0.0762627046050676 ; 2 : 0.572325279030854 ; 3 : -0.0742295791781891 ; 4 : 0.0658408653406101 ; 5 : -0.016034236226993 ; 6 : 3.27433486078147e-09 ; 7 : -0.000630588723767359 ; 8 : -5.65549557412152e-11 ; 9 : -1.3162188080067e-05 ; 10 : -2.96109552393859e-12 ;
Normalized w:
0 : 1 ; 1 : 0.0762627046050676 ; 2 : 0.809390171694399 ; 3 : -0.181824592808086 ; 4 : 0.322553048615586 ; 5 : -0.175646257477812 ; 6 : 8.78596239576562e-08 ; 7 : -0.0447673584015679 ; 8 : -1.13561449850589e-08 ; 9 : -0.00792883917238705 ; 10 : -5.64071210254656e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-9-2.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 639
Number of False Discoveries by ASH at lfsr = 0.05: 2300
pihat0 estimated by ASH: 0.04750946
Unnormalized w:
0 : 1 ; 1 : 0.0132006489023589 ; 2 : 0.752373085029163 ; 3 : 0.0203345251933944 ; 4 : 0.0867415022867811 ; 5 : -0.00760820428774983 ; 6 : -1.10494922428467e-09 ; 7 : -0.00294317971105688 ; 8 : -1.58067898541077e-11 ; 9 : -0.000164456475629658 ; 10 : 2.12731019116624e-13 ;
Normalized w:
0 : 1 ; 1 : 0.0132006489023589 ; 2 : 1.06401622081273 ; 3 : 0.0498092108855858 ; 4 : 0.424944840250148 ; 5 : -0.0833437022101621 ; 6 : -2.96488989262341e-08 ; 7 : -0.208945031839351 ; 8 : -3.17397821250152e-09 ; 9 : -0.0990677946700876 ; 10 : 4.05240028366978e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-9-3.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 1
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 0.9998824
Unnormalized w:
0 : 1 ; 1 : 0.108378799022329 ; 2 : -0.118544204689578 ; 3 : 0.149535650571497 ; 4 : 1.04844549405109e-09 ; 5 : 0.0707641605237991 ; 6 : -9.1503517984161e-11 ; 7 : 0.0127375051159948 ; 8 : 5.05937935302799e-13 ; 9 : 0.000656454459567348 ; 10 : -4.32761979200679e-14 ;
Normalized w:
0 : 1 ; 1 : 0.108378799022329 ; 2 : -0.167646822012733 ; 3 : 0.36628604225529 ; 4 : 5.13631296709075e-09 ; 5 : 0.775182539636027 ; 6 : -2.4552970367155e-09 ; 7 : 0.90427315804638 ; 8 : 1.01591531130008e-10 ; 9 : 0.395445028003221 ; 10 : -8.24386013171354e-11 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-9-4.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 1
Number of False Discoveries by ASH at lfsr = 0.05: 357
pihat0 estimated by ASH: 0.07619716
Unnormalized w:
0 : 1 ; 1 : 0.00731060610766733 ; 2 : 0.336253769001316 ; 3 : -0.014871486629131 ; 4 : 2.14561337556813e-07 ; 5 : -0.00280073551495972 ; 6 : -2.10100795862411e-09 ; 7 : -0.000291179301407538 ; 8 : 2.33753552855575e-11 ; 9 : -4.88929337454658e-05 ; 10 : -2.42600452715082e-13 ;
Normalized w:
0 : 1 ; 1 : 0.00731060610766733 ; 2 : 0.475534640520731 ; 3 : -0.0364275539579937 ; 4 : 1.05113159108651e-06 ; 5 : -0.0306805203829858 ; 6 : -5.63759594010189e-08 ; 7 : -0.0206716797397704 ; 8 : 4.69373408962992e-09 ; 9 : -0.0294528695362634 ; 10 : -4.62139535401769e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-9-5.png" width="672" style="display: block; margin: auto;" /></p>
</div>
</div>
<div id="hostile" class="section level2">
<h2>Hostile</h2>
<p>All “hostile” data sets are inflated.</p>
<div id="no-regularization-lambda-0-1" class="section level3">
<h3>No regularization: <span class="math inline">\(\lambda = 0\)</span></h3>
<pre class="r"><code>CorNullPlot("hostile", L, lambda = 0, rho)</code></pre>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 639
Number of False Discoveries by ASH at lfsr = 0.05: 2300
pihat0 estimated by ASH: 0.04750946
Unnormalized w:
0 : 1 ; 1 : 0.0227244539615043 ; 2 : 0.92101434792072 ; 3 : 0.0222103145256307 ; 4 : 0.175694879344268 ; 5 : -0.0134165085467778 ; 6 : 0.00392982154182872 ; 7 : -0.00480255115990118 ; 8 : -0.000586133715906366 ; 9 : -0.000291508028046953 ; 10 : 2.65975448800262e-06 ;
Normalized w:
0 : 1 ; 1 : 0.0227244539615043 ; 2 : 1.30251098196969 ; 3 : 0.0544039376145207 ; 4 : 0.860725609626624 ; 5 : -0.146970487480621 ; 6 : 0.105448177283665 ; 7 : -0.340947309892716 ; 8 : -0.117694716072657 ; 9 : -0.175603042426075 ; 10 : 0.00506667522509486 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-10-1.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 408
Number of False Discoveries by ASH at lfsr = 0.05: 2448
pihat0 estimated by ASH: 0.03139009
Unnormalized w:
0 : 1 ; 1 : 0.0154288916215935 ; 2 : 0.952920646422686 ; 3 : 0.0299159225977431 ; 4 : 0.141467724356241 ; 5 : 0.00918576726155382 ; 6 : -0.0084931811923254 ; 7 : 0.000415049492994605 ; 8 : -0.00154678887803449 ; 9 : 2.66655506029959e-05 ; 10 : -3.79757318599317e-05 ;
Normalized w:
0 : 1 ; 1 : 0.0154288916215935 ; 2 : 1.3476333020363 ; 3 : 0.0732787455490672 ; 4 : 0.693047479490981 ; 5 : 0.10062503874291 ; 6 : -0.227895965895148 ; 7 : 0.0294655909738936 ; 8 : -0.310592741697347 ; 9 : 0.0160632001980348 ; 10 : -0.0723415264970773 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-10-2.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 331
Number of False Discoveries by ASH at lfsr = 0.05: 1822
pihat0 estimated by ASH: 0.04301549
Unnormalized w:
0 : 1 ; 1 : 0.0071244364456378 ; 2 : 0.780475489960925 ; 3 : -0.110297574001406 ; 4 : 0.107848037343858 ; 5 : -0.0224625109915279 ; 6 : -0.0128392334784825 ; 7 : -0.000573937582144242 ; 8 : -0.00292373634747594 ; 9 : 1.6026836774617e-06 ; 10 : -0.000112993982390249 ;
Normalized w:
0 : 1 ; 1 : 0.0071244364456378 ; 2 : 1.10375902300253 ; 3 : -0.270172776170312 ; 4 : 0.528345322506156 ; 5 : -0.246064479365351 ; 6 : -0.344512786042534 ; 7 : -0.0407455263178155 ; 8 : -0.587081599213887 ; 9 : 0.000965448985039801 ; 10 : -0.215246863477015 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-10-3.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 114
Number of False Discoveries by ASH at lfsr = 0.05: 1685
pihat0 estimated by ASH: 0.02583276
Unnormalized w:
0 : 1 ; 1 : 0.0458630182725496 ; 2 : 0.756062141050916 ; 3 : 0.000522286088833344 ; 4 : 0.0893796469651393 ; 5 : -0.00182535146538549 ; 6 : -0.00670505702133343 ; 7 : 0.00155750252807623 ; 8 : -0.00152348453369753 ; 9 : 0.000174010174048529 ; 10 : -6.54073091086348e-05 ;
Normalized w:
0 : 1 ; 1 : 0.0458630182725496 ; 2 : 1.06923333387105 ; 3 : 0.00127933441739562 ; 4 : 0.437869056909381 ; 5 : -0.0199957234593349 ; 6 : -0.179915559512566 ; 7 : 0.11057171062174 ; 8 : -0.305913266493032 ; 9 : 0.104822896922382 ; 10 : -0.124597061155712 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-10-4.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 79
Number of False Discoveries by ASH at lfsr = 0.05: 1814
pihat0 estimated by ASH: 0.01606004
Unnormalized w:
0 : 1 ; 1 : 0.0352466614174826 ; 2 : 0.76764549272395 ; 3 : 0.0294087568867211 ; 4 : 0.063983964946533 ; 5 : -0.00272625339888582 ; 6 : -0.0166812243244297 ; 7 : -0.00175235100172814 ; 8 : -0.00249016360710572 ; 9 : -0.000110171636609466 ; 10 : -0.000108201442747287 ;
Normalized w:
0 : 1 ; 1 : 0.0352466614174826 ; 2 : 1.08561466690479 ; 3 : 0.0720364483420274 ; 4 : 0.313456131678262 ; 5 : -0.0298646096808979 ; 6 : -0.447604218448174 ; 7 : -0.124404580010619 ; 8 : -0.500020883902863 ; 9 : -0.0663668671744645 ; 10 : -0.206117358485555 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-10-5.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 35
Number of False Discoveries by ASH at lfsr = 0.05: 1137
pihat0 estimated by ASH: 0.04829662
Unnormalized w:
0 : 1 ; 1 : 0.0155701631204155 ; 2 : 0.610648478330274 ; 3 : 0.0551077467439953 ; 4 : 0.0685970418092259 ; 5 : 0.0169280711830408 ; 6 : 4.77079679243324e-05 ; 7 : 0.000459249911420758 ; 8 : 8.16221666285944e-05 ; 9 : -9.11879625666256e-05 ; 10 : 1.76195080904653e-05 ;
Normalized w:
0 : 1 ; 1 : 0.0155701631204155 ; 2 : 0.863587359897166 ; 3 : 0.134985860397309 ; 4 : 0.336055500593935 ; 5 : 0.185437728840093 ; 6 : 0.00128013911216624 ; 7 : 0.0326035093961596 ; 8 : 0.0163896009833396 ; 9 : -0.0549311926900185 ; 10 : 0.0335641223740764 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-10-6.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 28
Number of False Discoveries by ASH at lfsr = 0.05: 1653
pihat0 estimated by ASH: 0.02316832
Unnormalized w:
0 : 1 ; 1 : -0.0454462107392084 ; 2 : 0.731635414118698 ; 3 : -0.00197063805379626 ; 4 : 0.0671792199803835 ; 5 : -0.0152667648045991 ; 6 : -0.00791142637750884 ; 7 : -0.00214165049860173 ; 8 : -0.000257366565348708 ; 9 : 5.48859085063099e-06 ; 10 : 3.10611293325516e-05 ;
Normalized w:
0 : 1 ; 1 : -0.0454462107392084 ; 2 : 1.03468872535912 ; 3 : -0.00482705769951215 ; 4 : 0.329109620540248 ; 5 : -0.167239029272098 ; 6 : -0.212285846149136 ; 7 : -0.152042102606915 ; 8 : -0.0516787961744721 ; 9 : 0.003306300888041 ; 10 : 0.0591696170314166 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-10-7.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 16
Number of False Discoveries by ASH at lfsr = 0.05: 1506
pihat0 estimated by ASH: 0.05110069
Unnormalized w:
0 : 1 ; 1 : -0.0307690864088977 ; 2 : 0.712131187119833 ; 3 : -0.0222867102459425 ; 4 : 0.0797018945257774 ; 5 : -0.000212502676097517 ; 6 : -0.00304346991756197 ; 7 : 0.000776824043771723 ; 8 : -6.59826931703547e-05 ; 9 : 7.95517863468703e-05 ; 10 : 4.39916990470856e-05 ;
Normalized w:
0 : 1 ; 1 : -0.0307690864088977 ; 2 : 1.00710558301372 ; 3 : -0.0545910681478169 ; 4 : 0.390457946242557 ; 5 : -0.00232785018457648 ; 6 : -0.081664867477731 ; 7 : 0.055149036244603 ; 8 : -0.0132492196364877 ; 9 : 0.04792161576658 ; 10 : 0.0838015887094456 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-10-8.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 12
Number of False Discoveries by ASH at lfsr = 0.05: 795
pihat0 estimated by ASH: 0.04316169
Unnormalized w:
0 : 1 ; 1 : -0.0344695490777356 ; 2 : 0.522571163393063 ; 3 : 0.0313607610699586 ; 4 : 0.0339792130749094 ; 5 : 0.0103080681023228 ; 6 : -0.00198873199841041 ; 7 : 4.4467825695412e-05 ; 8 : 0.00021300079871282 ; 9 : -8.34952321992777e-06 ; 10 : 1.98696121319262e-05 ;
Normalized w:
0 : 1 ; 1 : -0.0344695490777356 ; 2 : 0.739027226575557 ; 3 : 0.0768178625667375 ; 4 : 0.166463467789669 ; 5 : 0.112919228478833 ; 6 : -0.0533632792496961 ; 7 : 0.00315690245514029 ; 8 : 0.0427702209366833 ; 9 : -0.00502971286948678 ; 10 : 0.0378504376908398 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-10-9.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 11
Number of False Discoveries by ASH at lfsr = 0.05: 1028
pihat0 estimated by ASH: 0.03156173
Unnormalized w:
0 : 1 ; 1 : 0.0104975596282685 ; 2 : 0.579125687844271 ; 3 : 0.0712077182038672 ; 4 : 0.0472520309498492 ; 5 : 0.00766045653227167 ; 6 : -0.0029999092141953 ; 7 : -0.00143274142610634 ; 8 : 0.000281761349107555 ; 9 : -9.24875783860482e-05 ; 10 : 6.5126905978099e-05 ;
Normalized w:
0 : 1 ; 1 : 0.0104975596282685 ; 2 : 0.819007402068015 ; 3 : 0.174422575347368 ; 4 : 0.231486730274658 ; 5 : 0.0839160968702599 ; 6 : -0.080496011151224 ; 7 : -0.101714551024765 ; 8 : 0.056577229876945 ; 9 : -0.0557140750463113 ; 10 : 0.124062909751538 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-10-10.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 9
Number of False Discoveries by ASH at lfsr = 0.05: 614
pihat0 estimated by ASH: 0.04794909
Unnormalized w:
0 : 1 ; 1 : -0.012281703930413 ; 2 : 0.484378296227544 ; 3 : 0.0440712708998003 ; 4 : 0.0237103488082757 ; 5 : 0.00836396915392277 ; 6 : -0.00537574147672548 ; 7 : -0.0013054623533153 ; 8 : -0.000847592148032516 ; 9 : -0.000133525903750732 ; 10 : -7.55297387329877e-05 ;
Normalized w:
0 : 1 ; 1 : -0.012281703930413 ; 2 : 0.685014355844165 ; 3 : 0.107952126020479 ; 4 : 0.116156512407366 ; 5 : 0.091622691517618 ; 6 : -0.144246280457079 ; 7 : -0.0926786332325558 ; 8 : -0.17019515257511 ; 9 : -0.0804353660460534 ; 10 : -0.143879691799561 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-10-11.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 7
Number of False Discoveries by ASH at lfsr = 0.05: 1307
pihat0 estimated by ASH: 0.05151585
Unnormalized w:
0 : 1 ; 1 : 0.0316501559909339 ; 2 : 0.63639003184346 ; 3 : 0.150623605408836 ; 4 : 0.0710578049167553 ; 5 : 0.0205410586065359 ; 6 : -0.00232338209328991 ; 7 : -0.00256591761351304 ; 8 : -0.000399841651727246 ; 9 : -0.000252319687963247 ; 10 : -2.53525509589763e-06 ;
Normalized w:
0 : 1 ; 1 : 0.0316501559909339 ; 2 : 0.899991413992067 ; 3 : 0.368950976469964 ; 4 : 0.348110728576561 ; 5 : 0.225016023076707 ; 6 : -0.0623428835796239 ; 7 : -0.182162079820845 ; 8 : -0.0802875664664511 ; 9 : -0.151996173715008 ; 10 : -0.00482951123557513 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-10-12.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 7
Number of False Discoveries by ASH at lfsr = 0.05: 689
pihat0 estimated by ASH: 0.04567195
Unnormalized w:
0 : 1 ; 1 : -0.0114149221900095 ; 2 : 0.494122018875004 ; 3 : 0.0407811769078796 ; 4 : 0.0293810611708229 ; 5 : 0.00420083938040471 ; 6 : -0.000169735520043324 ; 7 : -0.00059122469963324 ; 8 : 0.000651774557153136 ; 9 : -0.000106315927362571 ; 10 : 5.69253997014753e-05 ;
Normalized w:
0 : 1 ; 1 : -0.0114149221900095 ; 2 : 0.698794060560205 ; 3 : 0.0998930745344773 ; 4 : 0.143937215940032 ; 5 : 0.0460178897820737 ; 6 : -0.00455448193215781 ; 7 : -0.0419727899132323 ; 8 : 0.130875292387675 ; 9 : -0.0640442063578776 ; 10 : 0.108439524642999 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-10-13.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 6
Number of False Discoveries by ASH at lfsr = 0.05: 1392
pihat0 estimated by ASH: 0.0308234
Unnormalized w:
0 : 1 ; 1 : 0.0370556597109904 ; 2 : 0.682882414087328 ; 3 : 0.0463829983693932 ; 4 : 0.0372206294202173 ; 5 : 0.00893458882312159 ; 6 : -0.00365903877733973 ; 7 : -0.0015718648201254 ; 8 : 0.000865302913818613 ; 9 : -0.000182427628339264 ; 10 : 6.67747079772481e-05 ;
Normalized w:
0 : 1 ; 1 : 0.0370556597109904 ; 2 : 0.965741571508379 ; 3 : 0.113614678745358 ; 4 : 0.182343099969512 ; 5 : 0.0978735168091446 ; 6 : -0.0981823132612724 ; 7 : -0.111591332209313 ; 8 : 0.173751446120518 ; 9 : -0.109893531144151 ; 10 : 0.127201875247267 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-10-14.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 4
Number of False Discoveries by ASH at lfsr = 0.05: 1149
pihat0 estimated by ASH: 0.02083846
Unnormalized w:
0 : 1 ; 1 : -0.00719663878755195 ; 2 : 0.590959201932682 ; 3 : -0.0172003042045236 ; 4 : 0.00678574739612099 ; 5 : -0.0053623338822082 ; 6 : -0.00164100416474657 ; 7 : -0.000531083271301875 ; 8 : 0.00140201962800745 ; 9 : -8.24861592639277e-05 ; 10 : 4.67626846601773e-05 ;
Normalized w:
0 : 1 ; 1 : -0.00719663878755195 ; 2 : 0.83574251818238 ; 3 : -0.042131968721731 ; 4 : 0.0332432372878321 ; 5 : -0.0587414245631936 ; 6 : -0.0440327623648031 ; 7 : -0.0377031720538972 ; 8 : 0.281523307000802 ; 9 : -0.0496892679828852 ; 10 : 0.0890801526589662 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-10-15.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 1
Number of False Discoveries by ASH at lfsr = 0.05: 508
pihat0 estimated by ASH: 0.03271534
Unnormalized w:
0 : 1 ; 1 : 0.0111841878604641 ; 2 : 0.450895624947067 ; 3 : 0.038980313866716 ; 4 : 0.00296353543192371 ; 5 : 0.00351438732862135 ; 6 : -0.00390912755146694 ; 7 : -0.00142442285360721 ; 8 : -2.45080424286452e-05 ; 9 : -0.000143353997765883 ; 10 : 1.92180553113022e-05 ;
Normalized w:
0 : 1 ; 1 : 0.0111841878604641 ; 2 : 0.637662708014834 ; 3 : 0.0954818789869898 ; 4 : 0.0145182992857433 ; 5 : 0.0384981843139247 ; 6 : -0.104892899253569 ; 7 : -0.101123990961728 ; 8 : -0.00492117586287565 ; 9 : -0.0863557628936899 ; 10 : 0.0366092604259125 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-10-16.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 1
Number of False Discoveries by ASH at lfsr = 0.05: 662
pihat0 estimated by ASH: 0.02787007
Unnormalized w:
0 : 1 ; 1 : 0.0350137302803461 ; 2 : 0.470765168889938 ; 3 : -0.0160615011202655 ; 4 : -0.0399330192505554 ; 5 : 0.0329287497698357 ; 6 : -0.0240277513400892 ; 7 : 0.00930686045653883 ; 8 : -0.00274549884057576 ; 9 : 0.000566764428394551 ; 10 : -0.00012523163696814 ;
Normalized w:
0 : 1 ; 1 : 0.0350137302803461 ; 2 : 0.665762486537011 ; 3 : -0.0393424822477908 ; 4 : -0.195631042105197 ; 5 : 0.360716380787642 ; 6 : -0.644732224114812 ; 7 : 0.660721547892703 ; 8 : -0.551291791873294 ; 9 : 0.341416182023392 ; 10 : -0.238558872740559 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-10-17.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 1
Number of False Discoveries by ASH at lfsr = 0.05: 227
pihat0 estimated by ASH: 0.0531628
Unnormalized w:
0 : 1 ; 1 : 0.00286426406281591 ; 2 : 0.386810691223569 ; 3 : -0.0143590887965683 ; 4 : -0.0255496121929127 ; 5 : 0.00347603061961416 ; 6 : -4.76789154803652e-05 ; 7 : 0.001068930017731 ; 8 : 0.00076319617815179 ; 9 : 9.22925378517028e-05 ; 10 : 1.63550318067118e-07 ;
Normalized w:
0 : 1 ; 1 : 0.00286426406281591 ; 2 : 0.547032925599282 ; 3 : -0.035172440722907 ; 4 : -0.125167025997255 ; 5 : 0.0380780076188267 ; 6 : -0.00127935955329076 ; 7 : 0.0758865032093603 ; 8 : 0.153248576319164 ; 9 : 0.0555965835608901 ; 10 : 0.000311553697284798 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-10-18.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 1
Number of False Discoveries by ASH at lfsr = 0.05: 1340
pihat0 estimated by ASH: 0.03239883
Unnormalized w:
0 : 1 ; 1 : 0.0237520134361132 ; 2 : 0.651112971445468 ; 3 : 0.0517998517501412 ; 4 : 0.0324107063786448 ; 5 : 0.00273028493662741 ; 6 : -0.00897163791412935 ; 7 : -0.00341090892964708 ; 8 : -0.000654091985324589 ; 9 : -0.000329087147961516 ; 10 : -2.8333501939919e-05 ;
Normalized w:
0 : 1 ; 1 : 0.0237520134361132 ; 2 : 0.920812794855227 ; 3 : 0.12688320553966 ; 4 : 0.158779385661696 ; 5 : 0.0299087729641479 ; 6 : -0.240734306946092 ; 7 : -0.242150512328148 ; 8 : -0.131340628271375 ; 9 : -0.198240524600764 ; 10 : -0.0539736479313062 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-10-19.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 193
pihat0 estimated by ASH: 0.0465218
Unnormalized w:
0 : 1 ; 1 : 0.0232306825787541 ; 2 : 0.347387389370562 ; 3 : 0.0676187492916692 ; 4 : -0.0186668985504176 ; 5 : -1.39143386157503e-05 ; 6 : -0.00637803149808692 ; 7 : -0.00224350173369652 ; 8 : -0.00103131474862092 ; 9 : -0.000100620230928565 ; 10 : -9.227370323808e-05 ;
Normalized w:
0 : 1 ; 1 : 0.0232306825787541 ; 2 : 0.491279957445232 ; 3 : 0.165631432809771 ; 4 : -0.0914487530576442 ; 5 : -0.000152423942652233 ; 6 : -0.171140543908286 ; 7 : -0.159272823000851 ; 8 : -0.207086357987078 ; 9 : -0.0606131460565619 ; 10 : -0.175775955349633 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-10-20.png" width="672" style="display: block; margin: auto;" /></p>
</div>
<div id="lambda-1-1" class="section level3">
<h3><span class="math inline">\(\lambda = 1\)</span></h3>
<pre class="r"><code>CorNullPlot("hostile", L, lambda = 1, rho)</code></pre>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 639
Number of False Discoveries by ASH at lfsr = 0.05: 2300
pihat0 estimated by ASH: 0.04750946
Unnormalized w:
0 : 1 ; 1 : 0.0223556913438548 ; 2 : 0.916740955025879 ; 3 : 0.0218891094396244 ; 4 : 0.172881230445589 ; 5 : -0.0134617737282905 ; 6 : 0.00376825719933721 ; 7 : -0.00480328049020991 ; 8 : -0.000564405807267297 ; 9 : -0.000291745094113606 ; 10 : 8.09167312092846e-10 ;
Normalized w:
0 : 1 ; 1 : 0.0223556913438548 ; 2 : 1.29646749178046 ; 3 : 0.0536171490510185 ; 4 : 0.846941601392408 ; 5 : -0.147466342700302 ; 6 : 0.101112951053052 ; 7 : -0.340999087208252 ; 8 : -0.113331786644218 ; 9 : -0.175745849891238 ; 10 : 1.54141594332499e-06 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-11-1.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 408
Number of False Discoveries by ASH at lfsr = 0.05: 2448
pihat0 estimated by ASH: 0.03139009
Unnormalized w:
0 : 1 ; 1 : 0.0160250568304281 ; 2 : 0.9504830866948 ; 3 : 0.0320675120076468 ; 4 : 0.14407168991174 ; 5 : 0.0107790382487586 ; 6 : -0.00526204614013953 ; 7 : 0.000756481972585031 ; 8 : -0.000849111882761341 ; 9 : 4.68462535131963e-05 ; 10 : 1.29313347330595e-09 ;
Normalized w:
0 : 1 ; 1 : 0.0160250568304281 ; 2 : 1.34418607201003 ; 3 : 0.0785490417393073 ; 4 : 0.705804253328493 ; 5 : 0.118078447941122 ; 6 : -0.141195514441109 ; 7 : 0.0537048924514755 ; 8 : -0.170500312886761 ; 9 : 0.0282199591493084 ; 10 : 2.46334289931413e-06 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-11-2.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 331
Number of False Discoveries by ASH at lfsr = 0.05: 1822
pihat0 estimated by ASH: 0.04301549
Unnormalized w:
0 : 1 ; 1 : 0.00800939747755179 ; 2 : 0.772931414214873 ; 3 : -0.106128587896109 ; 4 : 0.106527061288674 ; 5 : -0.0193302012185171 ; 6 : -0.00828037456931695 ; 7 : 0.000169920604917084 ; 8 : -0.00139066109304468 ; 9 : 5.67707086212788e-05 ; 10 : -5.56172208067091e-10 ;
Normalized w:
0 : 1 ; 1 : 0.00800939747755179 ; 2 : 1.09309008876689 ; 3 : -0.259960887467581 ; 4 : 0.521873887910883 ; 5 : -0.211751744969913 ; 6 : -0.222185764993839 ; 7 : 0.0120631662657842 ; 8 : -0.2792425312816 ; 9 : 0.0341984034586349 ; 10 : -1.05947521104326e-06 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-11-3.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 114
Number of False Discoveries by ASH at lfsr = 0.05: 1685
pihat0 estimated by ASH: 0.02583276
Unnormalized w:
0 : 1 ; 1 : 0.0468410510368395 ; 2 : 0.755754656003814 ; 3 : 0.00152739035621532 ; 4 : 0.0950718054969482 ; 5 : -0.00162974613494927 ; 6 : -0.00174587263329282 ; 7 : 0.00157609614107534 ; 8 : -0.000428763024102919 ; 9 : 0.000175781331705588 ; 10 : 3.67761976479942e-11 ;
Normalized w:
0 : 1 ; 1 : 0.0468410510368395 ; 2 : 1.06879848434721 ; 3 : 0.00374132701077537 ; 4 : 0.465754824785304 ; 5 : -0.0178529744223714 ; 6 : -0.0468466786571918 ; 7 : 0.111891726197245 ; 8 : -0.0860949319494669 ; 9 : 0.105889833827275 ; 10 : 7.00564846630688e-08 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-11-4.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 79
Number of False Discoveries by ASH at lfsr = 0.05: 1814
pihat0 estimated by ASH: 0.01606004
Unnormalized w:
0 : 1 ; 1 : 0.0360981599057933 ; 2 : 0.766706667103251 ; 3 : 0.0330500715335886 ; 4 : 0.0707762394225816 ; 5 : 0.00105602955835814 ; 6 : -0.00976762391923616 ; 7 : -0.000675158695623136 ; 8 : -0.000810026978642787 ; 9 : -3.07395198886815e-05 ; 10 : -3.1752817001347e-12 ;
Normalized w:
0 : 1 ; 1 : 0.0360981599057933 ; 2 : 1.08428696697929 ; 3 : 0.0809558112197755 ; 4 : 0.34673134499676 ; 5 : 0.0115682242100995 ; 6 : -0.26209285274478 ; 7 : -0.0479315125147193 ; 8 : -0.162652126426702 ; 9 : -0.0185173398185105 ; 10 : -6.04872411921417e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-11-5.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 35
Number of False Discoveries by ASH at lfsr = 0.05: 1137
pihat0 estimated by ASH: 0.04829662
Unnormalized w:
0 : 1 ; 1 : 0.0155958690836745 ; 2 : 0.60877758371477 ; 3 : 0.0560325159085344 ; 4 : 0.0677202724819457 ; 5 : 0.0175329111032881 ; 6 : -0.000124217564025771 ; 7 : 0.00056431159268912 ; 8 : -4.73345914542686e-05 ; 9 : -8.61622929437318e-05 ; 10 : 1.50454483871259e-08 ;
Normalized w:
0 : 1 ; 1 : 0.0155958690836745 ; 2 : 0.860941515358149 ; 3 : 0.13725107298029 ; 4 : 0.331760225646016 ; 5 : 0.192063418200074 ; 6 : -0.00333310700593268 ; 7 : 0.0400621488585222 ; 8 : -0.00950471053010591 ; 9 : -0.0519037533363884 ; 10 : 2.86606906529709e-05 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-11-6.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 28
Number of False Discoveries by ASH at lfsr = 0.05: 1653
pihat0 estimated by ASH: 0.02316832
Unnormalized w:
0 : 1 ; 1 : -0.0467537900187071 ; 2 : 0.728715830709401 ; 3 : -0.00454531684862811 ; 4 : 0.0678560947849051 ; 5 : -0.0165052214031922 ; 6 : -0.00657507131583426 ; 7 : -0.00233869772539313 ; 8 : -8.57153442382681e-05 ; 9 : -3.28397506708893e-06 ; 10 : 3.01661943643426e-05 ;
Normalized w:
0 : 1 ; 1 : -0.0467537900187071 ; 2 : 1.03055981090521 ; 3 : -0.0111337069984141 ; 4 : 0.332425616321896 ; 5 : -0.180805641582909 ; 6 : -0.176427677029373 ; 7 : -0.166031067983752 ; 8 : -0.017211504524344 ; 9 : -0.00197825088007286 ; 10 : 0.0574648187682878 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-11-7.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 16
Number of False Discoveries by ASH at lfsr = 0.05: 1506
pihat0 estimated by ASH: 0.05110069
Unnormalized w:
0 : 1 ; 1 : -0.0308735233034481 ; 2 : 0.710414629721538 ; 3 : -0.0224290573030673 ; 4 : 0.0802203328578481 ; 5 : -8.15728257277138e-05 ; 6 : -0.00253347090141121 ; 7 : 0.00086434512182603 ; 8 : -0.000120288962542039 ; 9 : 8.86376362061075e-05 ; 10 : 2.82403852890122e-05 ;
Normalized w:
0 : 1 ; 1 : -0.0308735233034481 ; 2 : 1.00467800426046 ; 3 : -0.0549397458041594 ; 4 : 0.392997764995902 ; 5 : -0.000893585534610132 ; 6 : -0.0679801578548776 ; 7 : 0.061362416410269 ; 8 : -0.0241538319821229 ; 9 : 0.0533948882832861 ; 10 : 0.0537962662104288 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-11-8.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 12
Number of False Discoveries by ASH at lfsr = 0.05: 795
pihat0 estimated by ASH: 0.04316169
Unnormalized w:
0 : 1 ; 1 : -0.0344491971673983 ; 2 : 0.520936039054011 ; 3 : 0.031757736259423 ; 4 : 0.0329279384845785 ; 5 : 0.0104107162019601 ; 6 : -0.00254902120037916 ; 7 : 3.1968927166989e-05 ; 8 : -1.36409251995725e-07 ; 9 : -1.06924717257244e-05 ; 10 : 2.86812841151204e-10 ;
Normalized w:
0 : 1 ; 1 : -0.0344491971673983 ; 2 : 0.736714811559102 ; 3 : 0.07779024922147 ; 4 : 0.161313295137941 ; 5 : 0.114043682071961 ; 6 : -0.068397416161631 ; 7 : 0.00226956868440009 ; 8 : -2.73907604146168e-05 ; 9 : -0.00644109384798677 ; 10 : 5.46361524364291e-07 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-11-9.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 11
Number of False Discoveries by ASH at lfsr = 0.05: 1028
pihat0 estimated by ASH: 0.03156173
Unnormalized w:
0 : 1 ; 1 : 0.0102619591643994 ; 2 : 0.577204176450881 ; 3 : 0.0716691788973413 ; 4 : 0.0463837601494875 ; 5 : 0.00774791950289155 ; 6 : -0.00354664115712136 ; 7 : -0.0015028275036553 ; 8 : -6.98406544085581e-06 ; 9 : -0.000101225663517891 ; 10 : 3.45077259999144e-05 ;
Normalized w:
0 : 1 ; 1 : 0.0102619591643994 ; 2 : 0.816289974595229 ; 3 : 0.17555291858273 ; 4 : 0.227233089435769 ; 5 : 0.0848742057093583 ; 6 : -0.0951663686294624 ; 7 : -0.106690168942334 ; 8 : -0.00140238921049491 ; 9 : -0.0609778557538617 ; 10 : 0.0657351801404145 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-11-10.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 9
Number of False Discoveries by ASH at lfsr = 0.05: 614
pihat0 estimated by ASH: 0.04794909
Unnormalized w:
0 : 1 ; 1 : -0.0126799288193667 ; 2 : 0.486188521556034 ; 3 : 0.0437265990842193 ; 4 : 0.0284309423589625 ; 5 : 0.00940845797947052 ; 6 : -0.0020632828501766 ; 7 : -0.000839908561892715 ; 8 : 1.24668582342578e-08 ; 9 : -9.33124196200708e-05 ; 10 : -1.04035292420919e-05 ;
Normalized w:
0 : 1 ; 1 : -0.0126799288193667 ; 2 : 0.687574401054668 ; 3 : 0.107107855943588 ; 4 : 0.139282603371877 ; 5 : 0.10306449333391 ; 6 : -0.0553636885176527 ; 7 : -0.0596275927519892 ; 8 : 2.50332526585696e-06 ; 9 : -0.0562109554622068 ; 10 : -0.0198181088150137 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-11-11.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 7
Number of False Discoveries by ASH at lfsr = 0.05: 1307
pihat0 estimated by ASH: 0.05151585
Unnormalized w:
0 : 1 ; 1 : 0.0306804507050371 ; 2 : 0.634712838779934 ; 3 : 0.150255672592719 ; 4 : 0.0715689849145911 ; 5 : 0.0206710637611877 ; 6 : -0.00134610645675362 ; 7 : -0.00258223263719139 ; 8 : -0.000244952762316003 ; 9 : -0.000258568506140566 ; 10 : 9.58815036407773e-10 ;
Normalized w:
0 : 1 ; 1 : 0.0306804507050371 ; 2 : 0.897619504814911 ; 3 : 0.368049728810852 ; 4 : 0.35061498889939 ; 5 : 0.226440158192601 ; 6 : -0.0361198265070298 ; 7 : -0.183320331601776 ; 8 : -0.0491861243085364 ; 9 : -0.155760431910079 ; 10 : 1.8264860205439e-06 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-11-12.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 7
Number of False Discoveries by ASH at lfsr = 0.05: 689
pihat0 estimated by ASH: 0.04567195
Unnormalized w:
0 : 1 ; 1 : -0.0107395958908629 ; 2 : 0.49119549307977 ; 3 : 0.0425074224662843 ; 4 : 0.0259082103162259 ; 5 : 0.00474546555839352 ; 6 : -0.00238060698745243 ; 7 : -0.00063182892294805 ; 8 : 6.86094327098021e-09 ; 9 : -0.000116844928262916 ; 10 : 3.09442899779814e-06 ;
Normalized w:
0 : 1 ; 1 : -0.0107395958908629 ; 2 : 0.69465532808995 ; 3 : 0.104121495323315 ; 4 : 0.12692379084693 ; 5 : 0.0519839706439196 ; 6 : -0.0638783886198554 ; 7 : -0.0448554038091668 ; 8 : 1.3776664749953e-06 ; 9 : -0.0703868261621931 ; 10 : 0.00589470449610292 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-11-13.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 6
Number of False Discoveries by ASH at lfsr = 0.05: 1392
pihat0 estimated by ASH: 0.0308234
Unnormalized w:
0 : 1 ; 1 : 0.0395233563283826 ; 2 : 0.680264280751089 ; 3 : 0.0511438867100666 ; 4 : 0.0353532943160099 ; 5 : 0.0105267613164501 ; 6 : -0.0056843507574596 ; 7 : -0.00146725994667897 ; 8 : 8.65180076466989e-05 ; 9 : -0.000185202574268701 ; 10 : 2.45519292971495e-07 ;
Normalized w:
0 : 1 ; 1 : 0.0395233563283826 ; 2 : 0.962038971836169 ; 3 : 0.125276425902373 ; 4 : 0.173195063601322 ; 5 : 0.11531489260985 ; 6 : -0.152527136419585 ; 7 : -0.104165122885192 ; 8 : 0.017372678057607 ; 9 : -0.111565145305318 ; 10 : 0.000467699753715108 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-11-14.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 4
Number of False Discoveries by ASH at lfsr = 0.05: 1149
pihat0 estimated by ASH: 0.02083846
Unnormalized w:
0 : 1 ; 1 : -0.00733293919888795 ; 2 : 0.585506635320233 ; 3 : -0.0182658004946831 ; 4 : 0.000900817247036314 ; 5 : -0.00665105236070717 ; 6 : -0.00456309511180789 ; 7 : -0.000973246314961311 ; 8 : 0.000722084782573559 ; 9 : -0.000121189542456088 ; 10 : 7.11918933506316e-11 ;
Normalized w:
0 : 1 ; 1 : -0.00733293919888795 ; 2 : 0.828031424529312 ; 3 : -0.04474189095545 ; 4 : 0.00441308521347526 ; 5 : -0.0728586281821461 ; 6 : -0.122440690293593 ; 7 : -0.0690936341750258 ; 8 : 0.144993473603483 ; 9 : -0.0730040009810133 ; 10 : 1.35616352522115e-07 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-11-15.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 1
Number of False Discoveries by ASH at lfsr = 0.05: 508
pihat0 estimated by ASH: 0.03271534
Unnormalized w:
0 : 1 ; 1 : 0.0103611213527301 ; 2 : 0.449348604274889 ; 3 : 0.0376698222646347 ; 4 : 0.00233077225788051 ; 5 : 0.00299322662214977 ; 6 : -0.00389555766707583 ; 7 : -0.00149981007408626 ; 8 : -0.000113503792230453 ; 9 : -0.000146481027592927 ; 10 : 3.88311902097037e-06 ;
Normalized w:
0 : 1 ; 1 : 0.0103611213527301 ; 2 : 0.635474890398968 ; 3 : 0.0922718432496881 ; 4 : 0.0114184054768838 ; 5 : 0.0327891548135284 ; 6 : -0.104528781046225 ; 7 : -0.10647595269349 ; 8 : -0.0227913805966197 ; 9 : -0.0882394707114983 ; 10 : 0.00739711241334159 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-11-16.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 1
Number of False Discoveries by ASH at lfsr = 0.05: 662
pihat0 estimated by ASH: 0.02787007
Unnormalized w:
0 : 1 ; 1 : 0.0311809657713659 ; 2 : 0.479099518096388 ; 3 : -0.0340921650111574 ; 4 : -0.0190169406633145 ; 5 : 0.0149671032218498 ; 6 : -0.0123102633908051 ; 7 : 0.0041468828899631 ; 8 : -0.000554980614344054 ; 9 : 0.000172179597824328 ; 10 : -3.11742492225663e-08 ;
Normalized w:
0 : 1 ; 1 : 0.0311809657713659 ; 2 : 0.677549036218326 ; 3 : -0.0835084085041016 ; 4 : -0.0931636021878106 ; 5 : 0.163956401102308 ; 6 : -0.330319029153206 ; 7 : 0.294399480338309 ; 8 : -0.111439222925518 ; 9 : 0.103720166556717 ; 10 : -5.93851037414825e-05 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-11-17.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 1
Number of False Discoveries by ASH at lfsr = 0.05: 227
pihat0 estimated by ASH: 0.0531628
Unnormalized w:
0 : 1 ; 1 : 0.00268257272570874 ; 2 : 0.386084316089081 ; 3 : -0.0146004362562152 ; 4 : -0.0256328742061264 ; 5 : 0.00345646277117476 ; 6 : -0.000247660785930062 ; 7 : 0.00106365565313052 ; 8 : 0.0007123441528231 ; 9 : 9.08119481819637e-05 ; 10 : -6.80147235458954e-10 ;
Normalized w:
0 : 1 ; 1 : 0.00268257272570874 ; 2 : 0.54600567603272 ; 3 : -0.0357636188497589 ; 4 : -0.125574924891916 ; 5 : 0.0378636525789846 ; 6 : -0.00664543623240772 ; 7 : 0.075512060467981 ; 8 : 0.143037570672568 ; 9 : 0.0547046834223836 ; 10 : -1.29564031675139e-06 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-11-18.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 1
Number of False Discoveries by ASH at lfsr = 0.05: 1340
pihat0 estimated by ASH: 0.03239883
Unnormalized w:
0 : 1 ; 1 : 0.0226975128282614 ; 2 : 0.650247039913163 ; 3 : 0.0515460203709436 ; 4 : 0.0348890000926562 ; 5 : 0.00416045591030353 ; 6 : -0.00657513883441439 ; 7 : -0.00282017341343353 ; 8 : -0.000144622303014227 ; 9 : -0.000278135537474042 ; 10 : 2.60602458287274e-10 ;
Normalized w:
0 : 1 ; 1 : 0.0226975128282614 ; 2 : 0.919588182738155 ; 3 : 0.126261448179919 ; 4 : 0.170920495725845 ; 5 : 0.0455755110315787 ; 6 : -0.176429488742992 ; 7 : -0.200212450992589 ; 8 : -0.0290399279705525 ; 9 : -0.167547518037433 ; 10 : 4.96432292889751e-07 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-11-19.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 193
pihat0 estimated by ASH: 0.0465218
Unnormalized w:
0 : 1 ; 1 : 0.0214845657823466 ; 2 : 0.351396401277223 ; 3 : 0.063230593886195 ; 4 : -0.010037839370954 ; 5 : -0.00161352166619517 ; 6 : -0.00169194380273747 ; 7 : -0.00220701437405813 ; 8 : -2.20452212744048e-10 ; 9 : -7.64797879258848e-05 ; 10 : -1.69006427401707e-05 ;
Normalized w:
0 : 1 ; 1 : 0.0214845657823466 ; 2 : 0.496949556455348 ; 3 : 0.154882691154323 ; 4 : -0.0491751691577139 ; 5 : -0.0176752442719683 ; 6 : -0.0453996162843658 ; 7 : -0.156682477432507 ; 8 : -4.42664529993434e-08 ; 9 : -0.0460710586046817 ; 10 : -0.0321947263351014 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-11-20.png" width="672" style="display: block; margin: auto;" /></p>
</div>
<div id="lambda-10-1" class="section level3">
<h3><span class="math inline">\(\lambda = 10\)</span></h3>
<pre class="r"><code>CorNullPlot("hostile", L, lambda = 10, rho)</code></pre>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 639
Number of False Discoveries by ASH at lfsr = 0.05: 2300
pihat0 estimated by ASH: 0.04750946
Unnormalized w:
0 : 1 ; 1 : 0.0194979034611927 ; 2 : 0.881399833370166 ; 3 : 0.0202952891320483 ; 4 : 0.149606345019525 ; 5 : -0.0125010098851659 ; 6 : 0.00328865844826621 ; 7 : -0.00441151119171934 ; 8 : -7.86344085887155e-05 ; 9 : -0.000263759546136583 ; 10 : 4.02706012758681e-11 ;
Normalized w:
0 : 1 ; 1 : 0.0194979034611927 ; 2 : 1.24648759822547 ; 3 : 0.0497131025557711 ; 4 : 0.732918415161216 ; 5 : -0.136941702114008 ; 6 : 0.0882439661412266 ; 7 : -0.313186226090982 ; 8 : -0.0157896639303183 ; 9 : -0.15888748958586 ; 10 : 7.6713117208551e-08 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-12-1.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 408
Number of False Discoveries by ASH at lfsr = 0.05: 2448
pihat0 estimated by ASH: 0.03139009
Unnormalized w:
0 : 1 ; 1 : 0.0157245248645571 ; 2 : 0.929021872834485 ; 3 : 0.033984050303064 ; 4 : 0.140368261784685 ; 5 : 0.0127121650881182 ; 6 : 3.86030488190746e-09 ; 7 : 0.00124250846025535 ; 8 : -4.78228642870409e-09 ; 9 : 7.91371830919831e-05 ; 10 : 8.56994353557394e-11 ;
Normalized w:
0 : 1 ; 1 : 0.0157245248645571 ; 2 : 1.31383533230378 ; 3 : 0.0832435826355829 ; 4 : 0.687661234907779 ; 5 : 0.13925479146984 ; 6 : 1.03582849557833e-07 ; 7 : 0.0882093501845627 ; 8 : -9.60275493679947e-07 ; 9 : 0.0476718607480108 ; 10 : 1.63252363283959e-07 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-12-2.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 331
Number of False Discoveries by ASH at lfsr = 0.05: 1822
pihat0 estimated by ASH: 0.04301549
Unnormalized w:
0 : 1 ; 1 : 0.00892124119206404 ; 2 : 0.759107789311292 ; 3 : -0.117082898525434 ; 4 : 0.111843761652649 ; 5 : -0.0297056700788412 ; 6 : 7.95126961962164e-11 ; 7 : -0.00211837385159652 ; 8 : -0.000229022454624607 ; 9 : -8.25473971461178e-05 ; 10 : 1.35581200265726e-12 ;
Normalized w:
0 : 1 ; 1 : 0.00892124119206404 ; 2 : 1.07354053094709 ; 3 : -0.286793358993374 ; 4 : 0.547920293924901 ; 5 : -0.325409311759752 ; 6 : 2.13354952522835e-09 ; 7 : -0.150389624597725 ; 8 : -0.0459873439111496 ; 9 : -0.0497261573903446 ; 10 : 2.58274179618304e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-12-3.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 114
Number of False Discoveries by ASH at lfsr = 0.05: 1685
pihat0 estimated by ASH: 0.02583276
Unnormalized w:
0 : 1 ; 1 : 0.0480925696964731 ; 2 : 0.738515711602417 ; 3 : 0.00221250120053595 ; 4 : 0.0875509069264066 ; 5 : -0.00191476888655657 ; 6 : 1.55690130537233e-09 ; 7 : 0.00144844988545919 ; 8 : -7.20481946924742e-10 ; 9 : 0.000165048470111177 ; 10 : 1.38434287175444e-11 ;
Normalized w:
0 : 1 ; 1 : 0.0480925696964731 ; 2 : 1.04441893537376 ; 3 : 0.00541949899660829 ; 4 : 0.428910096975195 ; 5 : -0.0209752422315216 ; 6 : 4.17760458368483e-08 ; 7 : 0.102829741010377 ; 8 : -1.44671626759531e-07 ; 9 : 0.0994244093154905 ; 10 : 2.6370914168932e-08 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-12-4.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 79
Number of False Discoveries by ASH at lfsr = 0.05: 1814
pihat0 estimated by ASH: 0.01606004
Unnormalized w:
0 : 1 ; 1 : 0.036961161009979 ; 2 : 0.762234174397852 ; 3 : 0.0396536511894158 ; 4 : 0.0849620330092261 ; 5 : 0.00658028034188953 ; 6 : -0.00149261374799646 ; 7 : 0.000589489550662833 ; 8 : -2.63303502727629e-11 ; 9 : 4.91304899156167e-05 ; 10 : 1.39322722895517e-12 ;
Normalized w:
0 : 1 ; 1 : 0.036961161009979 ; 2 : 1.0779619071377 ; 3 : 0.0971312118523761 ; 4 : 0.41622725676421 ; 5 : 0.072083359559214 ; 6 : -0.0400510296560499 ; 7 : 0.0418496065562984 ; 8 : -5.28709237388671e-09 ; 9 : 0.029595972237431 ; 10 : 2.6540155926857e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-12-5.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 35
Number of False Discoveries by ASH at lfsr = 0.05: 1137
pihat0 estimated by ASH: 0.04829662
Unnormalized w:
0 : 1 ; 1 : 0.0140143989353616 ; 2 : 0.597743966910777 ; 3 : 0.0535575884068385 ; 4 : 0.0630838568812921 ; 5 : 0.0166752029879321 ; 6 : -5.24874438717071e-09 ; 7 : 0.000478996844103069 ; 8 : -4.43928396179664e-11 ; 9 : -8.77921415623364e-05 ; 10 : 4.86920576666347e-12 ;
Normalized w:
0 : 1 ; 1 : 0.0140143989353616 ; 2 : 0.845337624831916 ; 3 : 0.131188763450754 ; 4 : 0.309046520731854 ; 5 : 0.182667696549359 ; 6 : -1.4083859095481e-07 ; 7 : 0.0340054025468002 ; 8 : -8.91401144944578e-09 ; 9 : -0.0528855663520999 ; 10 : 9.27554942951506e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-12-6.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 28
Number of False Discoveries by ASH at lfsr = 0.05: 1653
pihat0 estimated by ASH: 0.02316832
Unnormalized w:
0 : 1 ; 1 : -0.052541093240518 ; 2 : 0.71740670301995 ; 3 : -0.0148451815829716 ; 4 : 0.0706308962096519 ; 5 : -0.0216927945431339 ; 6 : -0.00329645136528347 ; 7 : -0.00321089191984477 ; 8 : -5.51891940791841e-12 ; 9 : -4.485109559428e-05 ; 10 : 1.26313279205792e-12 ;
Normalized w:
0 : 1 ; 1 : -0.052541093240518 ; 2 : 1.01456628914818 ; 3 : -0.0363631200172426 ; 4 : 0.346019311578251 ; 5 : -0.237632658131989 ; 6 : -0.0884530720475501 ; 7 : -0.227950713272539 ; 8 : -1.10819022198443e-09 ; 9 : -0.0270180855575947 ; 10 : 2.40619337325787e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-12-7.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 16
Number of False Discoveries by ASH at lfsr = 0.05: 1506
pihat0 estimated by ASH: 0.05110069
Unnormalized w:
0 : 1 ; 1 : -0.0298742128887614 ; 2 : 0.699187239719963 ; 3 : -0.0203438591846129 ; 4 : 0.0800846069265758 ; 5 : 0.00139184678102155 ; 6 : -3.32097337202773e-09 ; 7 : 0.00127034253818031 ; 8 : -1.18095009628928e-10 ; 9 : 0.000121048879283542 ; 10 : 6.3863496996739e-12 ;
Normalized w:
0 : 1 ; 1 : -0.0298742128887614 ; 2 : 0.988800077050181 ; 3 : -0.0498320744013346 ; 4 : 0.39233284644294 ; 5 : 0.0152469175711291 ; 6 : -8.91110665358483e-08 ; 7 : 0.0901853736928798 ; 8 : -2.37132897335234e-08 ; 9 : 0.0729192661583677 ; 10 : 1.2165619025397e-08 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-12-8.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 12
Number of False Discoveries by ASH at lfsr = 0.05: 795
pihat0 estimated by ASH: 0.04316169
Unnormalized w:
0 : 1 ; 1 : -0.0340541695971239 ; 2 : 0.513452746960379 ; 3 : 0.0332197000452204 ; 4 : 0.032903765181378 ; 5 : 0.0113186061652928 ; 6 : -0.00161876973099202 ; 7 : 0.000233268302218612 ; 8 : 1.07332741281119e-09 ; 9 : 2.68357174057194e-06 ; 10 : -1.00292555933494e-11 ;
Normalized w:
0 : 1 ; 1 : -0.0340541695971239 ; 2 : 0.726131838389089 ; 3 : 0.0813713145191013 ; 4 : 0.161194870621464 ; 5 : 0.123989118324959 ; 6 : -0.0434361499010066 ; 7 : 0.016560406641522 ; 8 : 2.15522434003767e-07 ; 9 : 0.00161657078664457 ; 10 : -1.91051396172764e-08 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-12-9.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 11
Number of False Discoveries by ASH at lfsr = 0.05: 1028
pihat0 estimated by ASH: 0.03156173
Unnormalized w:
0 : 1 ; 1 : 0.00890469934508206 ; 2 : 0.570145988689668 ; 3 : 0.0742781809986447 ; 4 : 0.049710222895347 ; 5 : 0.0105652157303946 ; 6 : -0.000780824169897197 ; 7 : -0.000868342123034908 ; 8 : -9.34567110080382e-10 ; 9 : -6.17440887286602e-05 ; 10 : 1.36250969299168e-10 ;
Normalized w:
0 : 1 ; 1 : 0.00890469934508206 ; 2 : 0.806308189737545 ; 3 : 0.181943642468772 ; 4 : 0.243529362187236 ; 5 : 0.115736139608911 ; 6 : -0.0209517110683797 ; 7 : -0.0616461753468075 ; 8 : -1.87659586348254e-07 ; 9 : -0.0371943438581111 ; 10 : 2.59550050073108e-07 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-12-10.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 9
Number of False Discoveries by ASH at lfsr = 0.05: 614
pihat0 estimated by ASH: 0.04794909
Unnormalized w:
0 : 1 ; 1 : -0.0124963683703915 ; 2 : 0.479455691782456 ; 3 : 0.0437902382837533 ; 4 : 0.0283590951436181 ; 5 : 0.00932976751648813 ; 6 : -0.00148770349123624 ; 7 : -0.000860378572827223 ; 8 : 3.94801560648696e-09 ; 9 : -9.53163745720882e-05 ; 10 : -9.98282366267257e-11 ;
Normalized w:
0 : 1 ; 1 : -0.0124963683703915 ; 2 : 0.678052741875724 ; 3 : 0.107263739510085 ; 4 : 0.138930625337809 ; 5 : 0.10220248250119 ; 6 : -0.0399192736412158 ; 7 : -0.0610808193661828 ; 8 : 7.92755242099278e-07 ; 9 : -0.0574181283446029 ; 10 : -1.90166895314227e-07 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-12-11.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 7
Number of False Discoveries by ASH at lfsr = 0.05: 1307
pihat0 estimated by ASH: 0.05151585
Unnormalized w:
0 : 1 ; 1 : 0.0249866787261641 ; 2 : 0.622453028945155 ; 3 : 0.14478886016202 ; 4 : 0.0675724682587178 ; 5 : 0.020066114921205 ; 6 : -1.33026910243792e-08 ; 7 : -0.0024599148314936 ; 8 : -6.12782788990293e-10 ; 9 : -0.000245829910999426 ; 10 : 2.38424680814678e-11 ;
Normalized w:
0 : 1 ; 1 : 0.0249866787261641 ; 2 : 0.880281515474451 ; 3 : 0.354658827836135 ; 4 : 0.331036135788542 ; 5 : 0.219813275676699 ; 6 : -3.56948656970259e-07 ; 7 : -0.174636628832954 ; 8 : -1.23045807479098e-07 ; 9 : -0.148086763098947 ; 10 : 4.54184936536026e-08 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-12-12.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 7
Number of False Discoveries by ASH at lfsr = 0.05: 689
pihat0 estimated by ASH: 0.04567195
Unnormalized w:
0 : 1 ; 1 : -0.0111641599125746 ; 2 : 0.483366099358236 ; 3 : 0.0430333304341389 ; 4 : 0.0252239744266155 ; 5 : 0.0053145247650554 ; 6 : -0.00149181259538353 ; 7 : -0.000500470553509336 ; 8 : 1.30187220486791e-09 ; 9 : -0.000109169976941762 ; 10 : 8.26950723192313e-12 ;
Normalized w:
0 : 1 ; 1 : -0.0111641599125746 ; 2 : 0.683582893303798 ; 3 : 0.105409701496223 ; 4 : 0.12357173326044 ; 5 : 0.0582177019248137 ; 6 : -0.0400295324756155 ; 7 : -0.0355298846838391 ; 8 : 2.61413864032502e-07 ; 9 : -0.0657634721794694 ; 10 : 1.57529229125175e-08 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-12-13.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 6
Number of False Discoveries by ASH at lfsr = 0.05: 1392
pihat0 estimated by ASH: 0.0308234
Unnormalized w:
0 : 1 ; 1 : 0.0396883802556293 ; 2 : 0.67106650481609 ; 3 : 0.0512893461267695 ; 4 : 0.0343206332660759 ; 5 : 0.0105514758544046 ; 6 : -0.00535610846077317 ; 7 : -0.0015066089219249 ; 8 : 2.09359032358976e-09 ; 9 : -0.000190699294743056 ; 10 : -1.35217763257903e-11 ;
Normalized w:
0 : 1 ; 1 : 0.0396883802556293 ; 2 : 0.949031352365224 ; 3 : 0.125632727251578 ; 4 : 0.168136078302152 ; 5 : 0.11558562680857 ; 6 : -0.143719471357807 ; 7 : -0.106958623008449 ; 8 : 4.20389600564663e-07 ; 9 : -0.114876343439823 ; 10 : -2.57581853581548e-08 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-12-14.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 4
Number of False Discoveries by ASH at lfsr = 0.05: 1149
pihat0 estimated by ASH: 0.02083846
Unnormalized w:
0 : 1 ; 1 : -0.00598719228952374 ; 2 : 0.580917336155386 ; 3 : -0.0165349746829778 ; 4 : 0.000950465157557428 ; 5 : -0.00671289660355908 ; 6 : -0.00617523768078916 ; 7 : -0.00125345735224704 ; 8 : 0.000270706421193476 ; 9 : -0.000154093702661098 ; 10 : -9.37294496814268e-11 ;
Normalized w:
0 : 1 ; 1 : -0.00598719228952374 ; 2 : 0.821541175408597 ; 3 : -0.0405022508831337 ; 4 : 0.00465630930861943 ; 5 : -0.0735360979193824 ; 6 : -0.165699014777553 ; 7 : -0.0889866444072755 ; 8 : 0.0543574179692827 ; 9 : -0.0928253097771609 ; 10 : -1.78549066353598e-07 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-12-15.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 1
Number of False Discoveries by ASH at lfsr = 0.05: 508
pihat0 estimated by ASH: 0.03271534
Unnormalized w:
0 : 1 ; 1 : 0.00921377905881179 ; 2 : 0.44227129467301 ; 3 : 0.0372495054752143 ; 4 : 0.00273567450396983 ; 5 : 0.00394518920913478 ; 6 : -0.00222978584354968 ; 7 : -0.00106801649732043 ; 8 : -5.61894618061238e-11 ; 9 : -0.000106260001823252 ; 10 : 2.17619087094125e-11 ;
Normalized w:
0 : 1 ; 1 : 0.00921377905881179 ; 2 : 0.625466063174878 ; 3 : 0.0912422815852832 ; 4 : 0.0134020132741351 ; 5 : 0.0432173824693818 ; 6 : -0.0598314326573256 ; 7 : -0.0758216496937715 ; 8 : -1.12827543853553e-08 ; 9 : -0.0640105170803662 ; 10 : 4.14551509194212e-08 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-12-16.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 1
Number of False Discoveries by ASH at lfsr = 0.05: 662
pihat0 estimated by ASH: 0.02787007
Unnormalized w:
0 : 1 ; 1 : 0.0351655201412852 ; 2 : 0.477980299062328 ; 3 : -0.0317266100935275 ; 4 : -0.00766843242627895 ; 5 : 0.0126420659517014 ; 6 : -0.00662466864866664 ; 7 : 0.00302793885516535 ; 8 : 1.98536054334988e-11 ; 9 : 7.04066901859213e-05 ; 10 : 5.64394017027393e-12 ;
Normalized w:
0 : 1 ; 1 : 0.0351655201412852 ; 2 : 0.675966221481093 ; 3 : -0.0777140059973769 ; 4 : -0.0375674931427924 ; 5 : 0.138486893904298 ; 6 : -0.177758513121963 ; 7 : 0.214962334146066 ; 8 : 3.98657233170917e-09 ; 9 : 0.0424126535609731 ; 10 : 1.07513727156521e-08 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-12-17.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 1
Number of False Discoveries by ASH at lfsr = 0.05: 227
pihat0 estimated by ASH: 0.0531628
Unnormalized w:
0 : 1 ; 1 : 0.00154431090479713 ; 2 : 0.381972653262992 ; 3 : -0.0152915626373851 ; 4 : -0.0256118391191644 ; 5 : 0.00444072504619955 ; 6 : -0.00214165427285971 ; 7 : 0.00143888814188744 ; 8 : 0.00024743732335813 ; 9 : 0.000120611072083836 ; 10 : -9.14622234340302e-11 ;
Normalized w:
0 : 1 ; 1 : 0.00154431090479713 ; 2 : 0.540190906700158 ; 3 : -0.0374565258314013 ; 4 : -0.125471874432412 ; 5 : 0.0486457055896333 ; 6 : -0.0574666144610064 ; 7 : 0.102150924556344 ; 8 : 0.04968502020632 ; 9 : 0.0726555331943753 ; 10 : -1.74230134245697e-07 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-12-18.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 1
Number of False Discoveries by ASH at lfsr = 0.05: 1340
pihat0 estimated by ASH: 0.03239883
Unnormalized w:
0 : 1 ; 1 : 0.0225205134556117 ; 2 : 0.641457207632186 ; 3 : 0.0533352583485684 ; 4 : 0.0364851668184028 ; 5 : 0.00612535217697635 ; 6 : -0.00444687379603166 ; 7 : -0.00232291022077059 ; 8 : 2.94218456475473e-10 ; 9 : -0.000245725498327179 ; 10 : -2.50902898268473e-12 ;
Normalized w:
0 : 1 ; 1 : 0.0225205134556117 ; 2 : 0.907157482715412 ; 3 : 0.130644168253509 ; 4 : 0.178740083770822 ; 5 : 0.0670998711998665 ; 6 : -0.119322145143472 ; 7 : -0.164910266340676 ; 8 : 5.90785971843801e-08 ; 9 : -0.148023865404372 ; 10 : -4.77955203871478e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-12-19.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 193
pihat0 estimated by ASH: 0.0465218
Unnormalized w:
0 : 1 ; 1 : 0.0234366645597321 ; 2 : 0.351530157056736 ; 3 : 0.066259278805185 ; 4 : -0.00480114776628634 ; 5 : -0.00203790224616046 ; 6 : -0.000823976416513142 ; 7 : -0.00268310405895844 ; 8 : 1.90426127259697e-09 ; 9 : -0.000125066918170818 ; 10 : -3.02780954426344e-11 ;
Normalized w:
0 : 1 ; 1 : 0.0234366645597321 ; 2 : 0.49713871569278 ; 3 : 0.162301423797512 ; 4 : -0.0235207244142095 ; 5 : -0.0223241006042506 ; 6 : -0.0221096073501608 ; 7 : -0.190481492149878 ; 8 : 3.8237262884611e-07 ; 9 : -0.0753397135742388 ; 10 : -5.76779837139999e-08 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-12-20.png" width="672" style="display: block; margin: auto;" /></p>
</div>
<div id="lambda-100-1" class="section level3">
<h3><span class="math inline">\(\lambda = 100\)</span></h3>
<pre class="r"><code>CorNullPlot("hostile", L, lambda = 100, rho)</code></pre>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 639
Number of False Discoveries by ASH at lfsr = 0.05: 2300
pihat0 estimated by ASH: 0.04750946
Unnormalized w:
0 : 1 ; 1 : 0.0132006489023589 ; 2 : 0.752373085029163 ; 3 : 0.0203345251933944 ; 4 : 0.0867415022867811 ; 5 : -0.00760820428774983 ; 6 : -1.10494922428467e-09 ; 7 : -0.00294317971105688 ; 8 : -1.58067898541077e-11 ; 9 : -0.000164456475629658 ; 10 : 2.12731019116624e-13 ;
Normalized w:
0 : 1 ; 1 : 0.0132006489023589 ; 2 : 1.06401622081273 ; 3 : 0.0498092108855858 ; 4 : 0.424944840250148 ; 5 : -0.0833437022101621 ; 6 : -2.96488989262341e-08 ; 7 : -0.208945031839351 ; 8 : -3.17397821250152e-09 ; 9 : -0.0990677946700876 ; 10 : 4.05240028366978e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-13-1.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 408
Number of False Discoveries by ASH at lfsr = 0.05: 2448
pihat0 estimated by ASH: 0.03139009
Unnormalized w:
0 : 1 ; 1 : 0.0105834739058566 ; 2 : 0.804961786327664 ; 3 : 0.0261787584314404 ; 4 : 0.0926865453395142 ; 5 : 0.00989805656833703 ; 6 : -2.5354523725189e-09 ; 7 : 0.00095688222754701 ; 8 : 2.04811826297778e-11 ; 9 : 7.72597502545557e-05 ; 10 : -8.7238564600081e-13 ;
Normalized w:
0 : 1 ; 1 : 0.0105834739058566 ; 2 : 1.13838787541666 ; 3 : 0.0641246002566118 ; 4 : 0.454069484206296 ; 5 : 0.108427777158807 ; 6 : -6.80333263039845e-08 ; 7 : 0.0679318992143783 ; 8 : 4.11258883259499e-09 ; 9 : 0.0465409041825547 ; 10 : -1.66184313599561e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-13-2.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 331
Number of False Discoveries by ASH at lfsr = 0.05: 1822
pihat0 estimated by ASH: 0.04301549
Unnormalized w:
0 : 1 ; 1 : 0.0320131581939377 ; 2 : 0.649515689894355 ; 3 : -0.0900465711396185 ; 4 : 0.0650229035742284 ; 5 : -0.0206964966588597 ; 6 : -2.21942942133303e-10 ; 7 : -0.00135553600458204 ; 8 : -3.74724715625219e-12 ; 9 : -8.11909005353444e-05 ; 10 : -2.22930395954244e-13 ;
Normalized w:
0 : 1 ; 1 : 0.0320131581939377 ; 2 : 0.918553897622715 ; 3 : -0.220568152379291 ; 4 : 0.318545870702104 ; 5 : -0.226718761627755 ; 6 : -5.95535406883642e-09 ; 7 : -0.0962335098236571 ; 8 : -7.52441257243127e-10 ; 9 : -0.0489090103172832 ; 10 : -4.24669238907905e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-13-3.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 114
Number of False Discoveries by ASH at lfsr = 0.05: 1685
pihat0 estimated by ASH: 0.02583276
Unnormalized w:
0 : 1 ; 1 : 0.0478741427101273 ; 2 : 0.636744066444071 ; 3 : 0.00280039305560423 ; 4 : 0.0471915925960114 ; 5 : -0.00175976181128063 ; 6 : -1.19238687936139e-10 ; 7 : 0.0011904959700241 ; 8 : 1.02063407037529e-12 ; 9 : 0.000131391532916318 ; 10 : -3.43621756805811e-14 ;
Normalized w:
0 : 1 ; 1 : 0.0478741427101273 ; 2 : 0.900492094525801 ; 3 : 0.00685953406546381 ; 4 : 0.231190644019065 ; 5 : -0.019277224797491 ; 6 : -3.19950974127709e-09 ; 7 : 0.0845168296814539 ; 8 : 2.04941694816425e-10 ; 9 : 0.079149631259606 ; 10 : -6.5457915377709e-11 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-13-4.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 79
Number of False Discoveries by ASH at lfsr = 0.05: 1814
pihat0 estimated by ASH: 0.01606004
Unnormalized w:
0 : 1 ; 1 : 0.0295010267165937 ; 2 : 0.659217346324276 ; 3 : 0.0316891852491315 ; 4 : 0.0493837441677906 ; 5 : 0.00471433747948774 ; 6 : -2.37451148091981e-10 ; 7 : 0.000401980706948216 ; 8 : 1.94606595925071e-12 ; 9 : 3.81187051320671e-05 ; 10 : -1.35441607673461e-13 ;
Normalized w:
0 : 1 ; 1 : 0.0295010267165937 ; 2 : 0.932274111723392 ; 3 : 0.0776223342249036 ; 4 : 0.241929949598464 ; 5 : 0.0516429796241497 ; 6 : -6.37148290162847e-09 ; 7 : 0.0285377992028692 ; 8 : 3.90766943304903e-10 ; 9 : 0.0229625257300127 ; 10 : -2.58008263973824e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-13-5.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 35
Number of False Discoveries by ASH at lfsr = 0.05: 1137
pihat0 estimated by ASH: 0.04829662
Unnormalized w:
0 : 1 ; 1 : 0.00424558401539101 ; 2 : 0.511849996157535 ; 3 : 0.0374277614247891 ; 4 : 0.0281204777136469 ; 5 : 0.0113184645140339 ; 6 : -2.90301822299753e-09 ; 7 : 5.69592362256861e-05 ; 8 : 4.37033454229306e-11 ; 9 : -8.45744624616698e-05 ; 10 : -7.98561492042503e-13 ;
Normalized w:
0 : 1 ; 1 : 0.00424558401539101 ; 2 : 0.723865206466603 ; 3 : 0.0916789177053568 ; 4 : 0.137761643443482 ; 5 : 0.123987566613162 ; 6 : -7.78961530385176e-08 ; 7 : 0.00404370463074693 ; 8 : 8.77556211388247e-09 ; 9 : -0.0509472518452458 ; 10 : -1.52121248246675e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-13-6.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 28
Number of False Discoveries by ASH at lfsr = 0.05: 1653
pihat0 estimated by ASH: 0.02316832
Unnormalized w:
0 : 1 ; 1 : -0.0579073929769914 ; 2 : 0.624297610453676 ; 3 : -0.0095361725642879 ; 4 : 0.0443091090631803 ; 5 : -0.0181144765657234 ; 6 : -5.04721944409982e-11 ; 7 : -0.00249283417116588 ; 8 : 6.12226107696798e-13 ; 9 : -8.99258314026113e-07 ; 10 : -1.16057368162252e-14 ;
Normalized w:
0 : 1 ; 1 : -0.0579073929769914 ; 2 : 0.882890147660704 ; 3 : -0.0233587568816336 ; 4 : 0.217069416324243 ; 5 : -0.198434148648908 ; 6 : -1.35431109292391e-09 ; 7 : -0.176973670111852 ; 8 : 1.2293402676251e-10 ; 9 : -0.000541708909109335 ; 10 : -2.21082432461269e-11 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-13-7.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 16
Number of False Discoveries by ASH at lfsr = 0.05: 1506
pihat0 estimated by ASH: 0.05110069
Unnormalized w:
0 : 1 ; 1 : -0.0255909251559379 ; 2 : 0.600752193190829 ; 3 : -0.0163386802555427 ; 4 : 0.0405728780387057 ; 5 : 0.00103539670420155 ; 6 : -2.44797260617011e-09 ; 7 : 0.000832340077074178 ; 8 : 2.22226746125963e-11 ; 9 : 8.01163387009444e-05 ; 10 : -4.91281792152021e-13 ;
Normalized w:
0 : 1 ; 1 : -0.0255909251559379 ; 2 : 0.849591899235853 ; 3 : -0.0400214296965659 ; 4 : 0.198765697182005 ; 5 : 0.0113422026171538 ; 6 : -6.56859978534442e-08 ; 7 : 0.0590902836317055 ; 8 : 4.4622776474479e-09 ; 9 : 0.0482616994056085 ; 10 : -9.35862800895627e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-13-8.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 12
Number of False Discoveries by ASH at lfsr = 0.05: 795
pihat0 estimated by ASH: 0.04316169
Unnormalized w:
0 : 1 ; 1 : -0.0401783346044442 ; 2 : 0.442275121559582 ; 3 : 0.0256458281127914 ; 4 : 0.00801944125993727 ; 5 : 0.00883988432919291 ; 6 : -3.95773494187874e-09 ; 7 : 0.000148824574319465 ; 8 : 6.11514127702424e-11 ; 9 : 2.03215738949129e-05 ; 10 : -1.26491688747154e-12 ;
Normalized w:
0 : 1 ; 1 : -0.0401783346044442 ; 2 : 0.62547147520977 ; 3 : 0.0628191929074629 ; 4 : 0.0392870782181371 ; 5 : 0.0968360810567076 ; 6 : -1.06197172403604e-07 ; 7 : 0.0105654966643175 ; 8 : 1.22791062314273e-08 ; 9 : 0.012241618958975 ; 10 : -2.40959196965922e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-13-9.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 11
Number of False Discoveries by ASH at lfsr = 0.05: 1028
pihat0 estimated by ASH: 0.03156173
Unnormalized w:
0 : 1 ; 1 : -0.00713289775443022 ; 2 : 0.490130637935728 ; 3 : 0.0579248234639622 ; 4 : 0.018975962213149 ; 5 : 0.00726873754490585 ; 6 : -7.24970694698185e-09 ; 7 : -0.000689894217038701 ; 8 : 7.44854402225804e-11 ; 9 : -1.98960670986822e-05 ; 10 : -7.81088085699679e-13 ;
Normalized w:
0 : 1 ; 1 : -0.00713289775443022 ; 2 : 0.693149395503284 ; 3 : 0.141886260927502 ; 4 : 0.0929628496010994 ; 5 : 0.0796250303585931 ; 6 : -1.94530050604847e-07 ; 7 : -0.0489776307588 ; 8 : 1.49565576943263e-08 ; 9 : -0.0119852956992292 ; 10 : -1.48792667529374e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-13-10.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 9
Number of False Discoveries by ASH at lfsr = 0.05: 614
pihat0 estimated by ASH: 0.04794909
Unnormalized w:
0 : 1 ; 1 : -0.0216291449788825 ; 2 : 0.412382435293265 ; 3 : 0.0328952487332636 ; 4 : 0.00476671911085713 ; 5 : 0.00692737740690498 ; 6 : -4.67825631219419e-09 ; 7 : -0.000695071135321422 ; 8 : 8.4765279556321e-11 ; 9 : -5.62605303714553e-05 ; 10 : -2.18482832828739e-12 ;
Normalized w:
0 : 1 ; 1 : -0.0216291449788825 ; 2 : 0.583196832876181 ; 3 : 0.0805765743584305 ; 4 : 0.0233520591375462 ; 5 : 0.0758856174022701 ; 6 : -1.25530789562804e-07 ; 7 : -0.049345155497894 ; 8 : 1.70207330502624e-08 ; 9 : -0.0338910745200501 ; 10 : -4.16196893809255e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-13-11.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 7
Number of False Discoveries by ASH at lfsr = 0.05: 1307
pihat0 estimated by ASH: 0.05151585
Unnormalized w:
0 : 1 ; 1 : -0.00576684163508081 ; 2 : 0.533396059333378 ; 3 : 0.112031445464562 ; 4 : 0.0313056394050992 ; 5 : 0.013527135945386 ; 6 : -1.943881958565e-09 ; 7 : -0.00189092404907672 ; 8 : 2.15307400468982e-11 ; 9 : -0.000133799657639083 ; 10 : -3.69261244798069e-13 ;
Normalized w:
0 : 1 ; 1 : -0.00576684163508081 ; 2 : 0.754335941225627 ; 3 : 0.274419876534617 ; 4 : 0.153365685228119 ; 5 : 0.148182349914538 ; 6 : -5.21598263950411e-08 ; 7 : -0.134242290457436 ; 8 : 4.32333828934467e-09 ; 9 : -0.0806002740796074 ; 10 : -7.0342086423588e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-13-12.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 7
Number of False Discoveries by ASH at lfsr = 0.05: 689
pihat0 estimated by ASH: 0.04567195
Unnormalized w:
0 : 1 ; 1 : -0.0196084763181005 ; 2 : 0.41744821858852 ; 3 : 0.033978148075886 ; 4 : 0.00159291246628547 ; 5 : 0.00320468943817534 ; 6 : -7.15177316371031e-09 ; 7 : -0.000437503823423119 ; 8 : 1.05264756576142e-10 ; 9 : -8.59829439510085e-05 ; 10 : -1.91203575190933e-12 ;
Normalized w:
0 : 1 ; 1 : -0.0196084763181005 ; 2 : 0.590360932316373 ; 3 : 0.0832291251906506 ; 4 : 0.00780364549463543 ; 5 : 0.0351056139017439 ; 6 : -1.9190221144458e-07 ; 7 : -0.0310596902973876 ; 8 : 2.11369953672236e-08 ; 9 : -0.0517957143606207 ; 10 : -3.64231519013986e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-13-13.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 6
Number of False Discoveries by ASH at lfsr = 0.05: 1392
pihat0 estimated by ASH: 0.0308234
Unnormalized w:
0 : 1 ; 1 : 0.0355436726283037 ; 2 : 0.585233420234378 ; 3 : 0.0476532741151539 ; 4 : 0.0178494867394756 ; 5 : 0.0122996901187348 ; 6 : -2.66739447471334e-09 ; 7 : -0.000751737424430662 ; 8 : 2.77298665063982e-11 ; 9 : -0.00013791935465543 ; 10 : -7.00702380706679e-13 ;
Normalized w:
0 : 1 ; 1 : 0.0355436726283037 ; 2 : 0.82764504004945 ; 3 : 0.116726206155104 ; 4 : 0.0874442693645797 ; 5 : 0.134736354567089 ; 6 : -7.15737044191964e-08 ; 7 : -0.0533680629464834 ; 8 : 5.56811300328707e-09 ; 9 : -0.0830819598664138 ; 10 : -1.33479665454296e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-13-14.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 4
Number of False Discoveries by ASH at lfsr = 0.05: 1149
pihat0 estimated by ASH: 0.02083846
Unnormalized w:
0 : 1 ; 1 : -0.00969769073359043 ; 2 : 0.514996324871894 ; 3 : -0.0282187966040121 ; 4 : 9.64676465435185e-08 ; 5 : -0.0120747164945973 ; 6 : -2.24791804163654e-08 ; 7 : -0.00173122912010175 ; 8 : 1.92088522400817e-10 ; 9 : -0.000142282975799265 ; 10 : -3.47438547259262e-12 ;
Normalized w:
0 : 1 ; 1 : -0.00969769073359043 ; 2 : 0.728314787206133 ; 3 : -0.0691216528352123 ; 4 : 4.72593021437563e-07 ; 5 : -0.132271891991413 ; 6 : -6.031797058737e-07 ; 7 : -0.122905075168167 ; 8 : 3.8571069179702e-08 ; 9 : -0.0857105843814436 ; 10 : -6.6184991418641e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-13-15.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 1
Number of False Discoveries by ASH at lfsr = 0.05: 508
pihat0 estimated by ASH: 0.03271534
Unnormalized w:
0 : 1 ; 1 : 0.00654401496867742 ; 2 : 0.40702927663415 ; 3 : 0.0352668942739153 ; 4 : 2.73924919551974e-09 ; 5 : 0.0044439418035202 ; 6 : -2.34446864226924e-10 ; 7 : -0.000744264268223872 ; 8 : 3.409573903626e-12 ; 9 : -8.07206253491806e-05 ; 10 : -3.65500557341514e-14 ;
Normalized w:
0 : 1 ; 1 : 0.00654401496867742 ; 2 : 0.575626323298925 ; 3 : 0.0863858957837742 ; 4 : 1.34195256147054e-08 ; 5 : 0.0486809434005641 ; 6 : -6.29086950627678e-09 ; 7 : -0.0528375214862722 ; 8 : 6.8463700624263e-10 ; 9 : -0.0486257187934747 ; 10 : -6.96256976722428e-11 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-13-16.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 1
Number of False Discoveries by ASH at lfsr = 0.05: 662
pihat0 estimated by ASH: 0.02787007
Unnormalized w:
0 : 1 ; 1 : 0.0453588752881293 ; 2 : 0.438090234532152 ; 3 : -0.0291189579394965 ; 4 : 2.86793713120655e-09 ; 5 : 0.0110860517404839 ; 6 : -5.70878155827704e-10 ; 7 : 0.00236930640711469 ; 8 : 8.82670765931082e-12 ; 9 : 2.12285880554833e-05 ; 10 : -2.14657496309032e-13 ;
Normalized w:
0 : 1 ; 1 : 0.0453588752881293 ; 2 : 0.619553151218579 ; 3 : -0.0713265887933314 ; 4 : 1.40499651716749e-08 ; 5 : 0.121441612238648 ; 6 : -1.53182683596056e-08 ; 7 : 0.168204068821195 ; 8 : 1.7723888314674e-09 ; 9 : 0.0127879999529627 ; 10 : -4.08909853648414e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-13-17.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 1
Number of False Discoveries by ASH at lfsr = 0.05: 227
pihat0 estimated by ASH: 0.0531628
Unnormalized w:
0 : 1 ; 1 : -0.00364409182611866 ; 2 : 0.389125880616772 ; 3 : -0.0255220177701119 ; 4 : -4.63675182385451e-07 ; 5 : -1.39719095146074e-05 ; 6 : -1.263904769272e-09 ; 7 : 0.000725526774932154 ; 8 : 9.04561852541172e-11 ; 9 : 8.39572550250558e-05 ; 10 : -1.78894463147996e-12 ;
Normalized w:
0 : 1 ; 1 : -0.00364409182611866 ; 2 : 0.550307097838612 ; 3 : -0.0625159207430191 ; 4 : -2.27153520647256e-06 ; 5 : -0.00015305460025143 ; 6 : -3.39141237741406e-08 ; 7 : 0.051507291423283 ; 8 : 1.81634578451714e-08 ; 9 : 0.0505754490362338 ; 10 : -3.40783387499525e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-13-18.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 1
Number of False Discoveries by ASH at lfsr = 0.05: 1340
pihat0 estimated by ASH: 0.03239883
Unnormalized w:
0 : 1 ; 1 : 0.0149991776855961 ; 2 : 0.559603231383086 ; 3 : 0.0465049266719185 ; 4 : 0.0184397682568843 ; 5 : 0.00703650419080853 ; 6 : -1.03776921070471e-09 ; 7 : -0.00149386108442593 ; 8 : 1.3106876747849e-11 ; 9 : -0.000178408010293136 ; 10 : -3.29469209420909e-13 ;
Normalized w:
0 : 1 ; 1 : 0.0149991776855961 ; 2 : 0.791398479369769 ; 3 : 0.113913340871748 ; 4 : 0.0903360464090738 ; 5 : 0.0770810414257094 ; 6 : -2.78462700011043e-08 ; 7 : -0.106053616323978 ; 8 : 2.63183996343221e-09 ; 9 : -0.107472132450538 ; 10 : -6.27619386802165e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-13-19.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 193
pihat0 estimated by ASH: 0.0465218
Unnormalized w:
0 : 1 ; 1 : 0.0226849154498927 ; 2 : 0.335107595160482 ; 3 : 0.0658274203844355 ; 4 : -1.28338913347439e-08 ; 5 : -0.00247141282053187 ; 6 : -2.49427997598805e-10 ; 7 : -0.00298977044563244 ; 8 : 1.268457383768e-11 ; 9 : -0.000163497363465059 ; 10 : -4.22926284937891e-13 ;
Normalized w:
0 : 1 ; 1 : 0.0226849154498927 ; 2 : 0.473913705930186 ; 3 : 0.161243591025551 ; 4 : -6.28729703688982e-08 ; 5 : -0.0270729710142555 ; 6 : -6.69285549747098e-09 ; 7 : -0.212252645874178 ; 8 : 2.54704221206563e-09 ; 9 : -0.0984900300875476 ; 10 : -8.05649596457834e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-13-20.png" width="672" style="display: block; margin: auto;" /></p>
</div>
</div>
<div id="friendly" class="section level2">
<h2>Friendly</h2>
<p>A good part of “friendly” data sets are deflated.</p>
<div id="no-regularization-lambda-0-2" class="section level3">
<h3>No regularization: <span class="math inline">\(\lambda = 0\)</span></h3>
<pre class="r"><code>CorNullPlot("friendly", L, lambda = 0, rho)</code></pre>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 137264954.214438 ; 2 : -722937240.714833 ; 3 : 418842016.840356 ; 4 : -1016772968.34235 ; 5 : 240045934.151314 ; 6 : -374946652.070722 ; 7 : 41386034.8214318 ; 8 : -47114090.7012788 ; 9 : 2040876.13279973 ; 10 : -1807482.83610991 ;
Normalized w:
0 : 1 ; 1 : 137264954.214438 ; 2 : -1022387650.5635 ; 3 : 1025949224.09707 ; 4 : -4981149913.38756 ; 5 : 2629571459.44149 ; 6 : -10060874423.5932 ; 7 : 2938117006.91675 ; 8 : -9460434330.30259 ; 9 : 1229414025.18311 ; 10 : -3443148060.02248 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-14-1.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -106261819.01034 ; 2 : -1150357596.48619 ; 3 : -232331281.30916 ; 4 : -1340627938.14957 ; 5 : -112068963.548569 ; 6 : -456263013.117482 ; 7 : -17279425.242415 ; 8 : -54979962.6558813 ; 9 : -796936.796482575 ; 10 : -2072478.27497457 ;
Normalized w:
0 : 1 ; 1 : -106261819.01034 ; 2 : -1626851314.52968 ; 3 : -569093090.49446 ; 4 : -6567708766.77187 ; 5 : -1227653986.63551 ; 6 : -12242821355.3948 ; 7 : -1226717500.08279 ; 8 : -11039888883.4829 ; 9 : -480070916.129586 ; 10 : -3947948721.48013 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-14-2.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -419300836.933388 ; 2 : -1694585535.52468 ; 3 : -810682683.439507 ; 4 : -1975460074.67748 ; 5 : -352299236.564591 ; 6 : -662240105.602199 ; 7 : -48370939.631651 ; 8 : -77601017.7932235 ; 9 : -1837301.55401029 ; 10 : -2799846.58349772 ;
Normalized w:
0 : 1 ; 1 : -419300836.933388 ; 2 : -2396505846.94028 ; 3 : -1985758917.73701 ; 4 : -9677738380.40037 ; 5 : -3859244777.16551 ; 6 : -17769766722.6379 ; 7 : -3433996056.53211 ; 8 : -15582160705.4279 ; 9 : -1106781672.18913 ; 10 : -5333542393.72954 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-14-3.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -89489789.7327784 ; 2 : -726111664.311445 ; 3 : -272260748.650809 ; 4 : -1053172284.98039 ; 5 : -156103245.723899 ; 6 : -394990362.858399 ; 7 : -26803318.7269033 ; 8 : -50144491.564265 ; 9 : -1312898.58614155 ; 10 : -1939839.37563693 ;
Normalized w:
0 : 1 ; 1 : -89489789.7327784 ; 2 : -1026876963.46655 ; 3 : -666899911.182626 ; 4 : -5159469418.88598 ; 5 : -1710025379.65503 ; 6 : -10598703621.7043 ; 7 : -1902846864.48249 ; 8 : -10068933994.247 ; 9 : -790883831.460775 ; 10 : -3695279451.36922 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-14-4.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 112889894.796798 ; 2 : -742338300.549163 ; 3 : 348258998.62458 ; 4 : -1034780345.77285 ; 5 : 201205933.841486 ; 6 : -381144424.471816 ; 7 : 34878380.5459064 ; 8 : -48017141.8842725 ; 9 : 1727489.57462506 ; 10 : -1850641.97462528 ;
Normalized w:
0 : 1 ; 1 : 112889894.796798 ; 2 : -1049824892.50562 ; 3 : 853056844.962849 ; 4 : -5069367686.00843 ; 5 : 2204100573.37748 ; 6 : -10227178108.3682 ; 7 : 2476119384.1787 ; 8 : -9641765568.71662 ; 9 : 1040631460.80706 ; 10 : -3525363670.08672 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-14-5.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.0470784370671212 ; 2 : -0.522631688675864 ; 3 : -0.0953426864633527 ; 4 : -0.740438283008238 ; 5 : -0.0559007315179676 ; 6 : -0.323435338420103 ; 7 : -0.0120562733702888 ; 8 : -0.0484360784107513 ; 9 : -0.000623238470056528 ; 10 : -0.00232871526180744 ;
Normalized w:
0 : 1 ; 1 : -0.0470784370671212 ; 2 : -0.73911282225136 ; 3 : -0.233540932541375 ; 4 : -3.62739195878534 ; 5 : -0.612361832668617 ; 6 : -8.67868083639599 ; 7 : -0.855910501745851 ; 8 : -9.72588735560298 ; 9 : -0.375435874724077 ; 10 : -4.43606504905667 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-14-6.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.00193985466749854 ; 2 : -0.0459043485242219 ; 3 : -0.0122824286035569 ; 4 : -0.00607306381602981 ; 5 : 0.00351725498554623 ; 6 : 0.0013871020433342 ; 7 : 0.000277482321742012 ; 8 : 1.13547480823551e-05 ; 9 : 6.74311181102265e-05 ; 10 : -3.01075670970948e-06 ;
Normalized w:
0 : 1 ; 1 : -0.00193985466749854 ; 2 : -0.0649185522548561 ; 3 : -0.0300856828808792 ; 4 : -0.0297518150492654 ; 5 : 0.0385295979216235 ; 6 : 0.0372198535274896 ; 7 : 0.0196992906459055 ; 8 : 0.00228001531964903 ; 9 : 0.0406201831684736 ; 10 : -0.00573531372864746 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-14-7.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 2.02099465369633 ; 2 : -12.7500510381693 ; 3 : 6.38103409252514 ; 4 : -19.5151088875592 ; 5 : 3.76180647511564 ; 6 : -7.60904274513008 ; 7 : 0.668035566785343 ; 8 : -1.00409684615153 ; 9 : 0.03413427725234 ; 10 : -0.0406102718894945 ;
Normalized w:
0 : 1 ; 1 : 2.02099465369633 ; 2 : -18.0312950991282 ; 3 : 15.6302775579901 ; 4 : -95.604118098746 ; 5 : 41.2085252677967 ; 6 : -204.17204186175 ; 7 : 47.4258205326031 ; 8 : -201.621046546541 ; 9 : 20.5623254243983 ; 10 : -77.3601696679102 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-14-8.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.00956223065055579 ; 2 : -0.139729871584823 ; 3 : -0.0126291983086343 ; 4 : -0.0264973264835549 ; 5 : -0.0135840230877693 ; 6 : -0.0171736274688293 ; 7 : -0.00307870144367361 ; 8 : -0.00289615242500924 ; 9 : -0.000290457029780478 ; 10 : -0.000167919884508643 ;
Normalized w:
0 : 1 ; 1 : 0.00956223065055579 ; 2 : -0.197607879463907 ; 3 : -0.0309350917165744 ; 4 : -0.12980985886529 ; 5 : -0.148805517336844 ; 6 : -0.46081678128672 ; 7 : -0.218566120429404 ; 8 : -0.58154279154119 ; 9 : -0.174969926095063 ; 10 : -0.319877463306641 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-14-9.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -594780833.462949 ; 2 : -1270269526.86431 ; 3 : -1419762879.07984 ; 4 : -1225019415.59396 ; 5 : -679108078.765335 ; 6 : -325170028.421899 ; 7 : -98308952.1848364 ; 8 : -27646118.6308513 ; 9 : -3938191.62464207 ; 10 : -573780.43118111 ;
Normalized w:
0 : 1 ; 1 : -594780833.462949 ; 2 : -1796432392.76076 ; 3 : -3477694609.49039 ; 4 : -6001344986.41527 ; 5 : -7439256274.47538 ; 6 : -8725227453.56286 ; 7 : -6979243254.22101 ; 8 : -5551296563.34054 ; 9 : -2372347806.6019 ; 10 : -1093017836.20365 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-14-10.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 541173520.168442 ; 2 : -1829704125.01795 ; 3 : 1176846048.20616 ; 4 : -2016580491.23649 ; 5 : 536195866.719198 ; 6 : -626478339.28782 ; 7 : 74728716.7247109 ; 8 : -66565470.6376099 ; 9 : 2831468.61953214 ; 10 : -2084985.52075391 ;
Normalized w:
0 : 1 ; 1 : 541173520.168442 ; 2 : -2587592388.73039 ; 3 : 2882672323.91591 ; 4 : -9879186457.56089 ; 5 : 5873731428.86276 ; 6 : -16810177836.9449 ; 7 : 5305212602.78448 ; 8 : -13366240423.1798 ; 9 : 1705663159.45067 ; 10 : -3971774286.06145 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-14-11.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -56432232.5590155 ; 2 : -942778323.786737 ; 3 : -117054726.547689 ; 4 : -996286639.780001 ; 5 : -54991463.4341151 ; 6 : -316578729.109756 ; 7 : -8028402.56625314 ; 8 : -35258958.3436016 ; 9 : -342254.887985098 ; 10 : -1218041.30050927 ;
Normalized w:
0 : 1 ; 1 : -56432232.5590155 ; 2 : -1333289891.81058 ; 3 : -286724352.022854 ; 4 : -4880787810.02606 ; 5 : -602401299.861707 ; 6 : -8494698702.23887 ; 7 : -569960041.353543 ; 8 : -7079942645.59718 ; 9 : -206172708.237381 ; 10 : -2320296744.78231 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-14-12.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -1.95677009214905 ; 2 : -12.2569463569483 ; 3 : -6.0748809266641 ; 4 : -18.9489453242006 ; 5 : -3.56745776349149 ; 6 : -7.40452267280642 ; 7 : -0.632340146447155 ; 8 : -0.979899114651218 ; 9 : -0.0321248697380335 ; 10 : -0.0397131144151632 ;
Normalized w:
0 : 1 ; 1 : -1.95677009214905 ; 2 : -17.3339397712759 ; 3 : -14.8803585184929 ; 4 : -92.8304944163773 ; 5 : -39.0795418002244 ; 6 : -198.684192448003 ; 7 : -44.8916970772592 ; 8 : -196.762180623553 ; 9 : -19.3518679445473 ; 10 : -75.6511376618707 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-14-13.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 7.92438556157571 ; 2 : -16.5970527053141 ; 3 : 24.2623695599727 ; 4 : -23.6100003489604 ; 5 : 14.0732466851824 ; 6 : -8.4629472072654 ; 7 : 2.45683144457811 ; 8 : -1.01755591322698 ; 9 : 0.12335441226633 ; 10 : -0.036891785992626 ;
Normalized w:
0 : 1 ; 1 : 7.92438556157571 ; 2 : -23.4717770312763 ; 3 : 59.4304253727679 ; 4 : -115.664907363771 ; 5 : 154.164693336184 ; 6 : -227.084702945249 ; 7 : 174.417730077024 ; 8 : -204.323605766494 ; 9 : 74.308108204687 ; 10 : -70.2766736334032 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-14-14.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 2074419142.47283 ; 2 : -3573068586.86138 ; 3 : 4229152806.46 ; 4 : -2931614091.00329 ; 5 : 1490639188.00118 ; 6 : -493475675.41199 ; 7 : 116534592.449922 ; 8 : -3852453.55778051 ; 9 : -642084.639127706 ; 10 : 1572783.00239395 ;
Normalized w:
0 : 1 ; 1 : 2074419142.47283 ; 2 : -5053082054.82863 ; 3 : 10359266420.0865 ; 4 : -14361917291.4224 ; 5 : 16329134167.3886 ; 6 : -13241341865.566 ; 7 : 8273135357.09687 ; 8 : -773566535.009745 ; 9 : -386788716.87099 ; 10 : 2996058737.23481 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-14-15.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 618987692.527178 ; 2 : -1801617642.29182 ; 3 : 1634174783.76893 ; 4 : -2191247482.97095 ; 5 : 887369121.590212 ; 6 : -748173277.136419 ; 7 : 147704383.115058 ; 8 : -88172740.9916949 ; 9 : 7183741.46857466 ; 10 : -3199467.88204137 ;
Normalized w:
0 : 1 ; 1 : 618987692.527178 ; 2 : -2547872103.93973 ; 3 : 4002894370.75692 ; 4 : -10734876466.8736 ; 5 : 9720641694.57007 ; 6 : -20075595679.5099 ; 7 : 10485970977.8663 ; 8 : -17704945876.2465 ; 9 : 4327451515.95236 ; 10 : -6094797367.40641 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-14-16.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.00984700926515223 ; 2 : -0.14656240112422 ; 3 : -0.0118379136012733 ; 4 : 0.010345781454132 ; 5 : -0.0011892934303944 ; 6 : -0.000753308229453712 ; 7 : -0.000550648736682494 ; 8 : -0.000132519405015875 ; 9 : -4.83894388687729e-05 ; 10 : -2.69726822353638e-06 ;
Normalized w:
0 : 1 ; 1 : 0.00984700926515223 ; 2 : -0.207270535403837 ; 3 : -0.0289968479422725 ; 4 : 0.0506837711059456 ; 5 : -0.0130280567863943 ; 6 : -0.0202133809088221 ; 7 : -0.0390921823041198 ; 8 : -0.0266096853400468 ; 9 : -0.0291495666296999 ; 10 : -0.00513813667587426 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-14-17.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -1014237.02898209 ; 2 : -597951917.012121 ; 3 : -2677628.90712859 ; 4 : -672071077.344696 ; 5 : -927136.046849423 ; 6 : -223161520.271774 ; 7 : -135927.093818087 ; 8 : -26093284.1988066 ; 9 : -6567.46435896308 ; 10 : -950757.022531773 ;
Normalized w:
0 : 1 ; 1 : -1014237.02898209 ; 2 : -845631710.685534 ; 3 : -6558824.54299121 ; 4 : -3292462420.75415 ; 5 : -10156266.5347119 ; 6 : -5988051951.4786 ; 7 : -9649866.380552 ; 8 : -5239489884.03232 ; 9 : -3956209.13147879 ; 10 : -1811135979.98446 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-14-18.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.0403717474792552 ; 2 : -0.229979607667662 ; 3 : 0.0189204963837437 ; 4 : -0.0173306848000264 ; 5 : 0.0141130226810881 ; 6 : -0.0231338566722466 ; 7 : 0.00350234700086261 ; 8 : -0.00330846703656365 ; 9 : 0.000289669799494303 ; 10 : -0.000209805713849822 ;
Normalized w:
0 : 1 ; 1 : -0.0403717474792552 ; 2 : -0.32524028023285 ; 3 : 0.0463455618203464 ; 4 : -0.0849026693061461 ; 5 : 0.15460041754028 ; 6 : -0.620746513210565 ; 7 : 0.248641971422434 ; 8 : -0.66433490846363 ; 9 : 0.174495702334337 ; 10 : -0.399667494590647 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-14-19.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 254386788.899495 ; 2 : -971207864.341701 ; 3 : 766962554.079245 ; 4 : -1422015137.03137 ; 5 : 436058921.203189 ; 6 : -527639757.022056 ; 7 : 74048282.6100759 ; 8 : -65810466.7577094 ; 9 : 3571375.30780089 ; 10 : -2484460.4768662 ;
Normalized w:
0 : 1 ; 1 : 254386788.899495 ; 2 : -1373495333.63544 ; 3 : 1878666909.3159 ; 4 : -6966422984.4815 ; 5 : 4776786150.88709 ; 6 : -14158060371.9935 ; 7 : 5256906572.6726 ; 8 : -13214636847.294 ; 9 : 2151379411.04724 ; 10 : -4732750486.04897 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-14-20.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 4.57639504918881 ; 2 : -57.5764820561853 ; 3 : 13.8021136775458 ; 4 : -87.1897901256237 ; 5 : 7.92280745858439 ; 6 : -33.4062693534841 ; 7 : 1.36236273420077 ; 8 : -4.30800695157544 ; 9 : 0.0667879534755144 ; 10 : -0.168853283481368 ;
Normalized w:
0 : 1 ; 1 : 4.57639504918881 ; 2 : -81.4254417975884 ; 3 : 33.8081358818758 ; 4 : -427.140993176266 ; 5 : 86.790007276737 ; 6 : -896.3842697887 ; 7 : 96.7181595486419 ; 8 : -865.040930499382 ; 9 : 40.2327438674259 ; 10 : -321.655533226841 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-14-21.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -843569484.171597 ; 2 : -2345053461.51224 ; 3 : -2329106746.43836 ; 4 : -2884547641.49376 ; 5 : -1293771901.31835 ; 6 : -978697186.533303 ; 7 : -219384288.369108 ; 8 : -114612626.09425 ; 9 : -10793693.7396976 ; 10 : -4120637.71361765 ;
Normalized w:
0 : 1 ; 1 : -843569484.171597 ; 2 : -3316406409.76059 ; 3 : -5705123085.24786 ; 4 : -14131339720.8167 ; 5 : -14172561092.3681 ; 6 : -26261201261.7151 ; 7 : -15574739437.8021 ; 8 : -23014032669.3972 ; 9 : -6502069505.27235 ; 10 : -7849571495.92278 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-14-22.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -7152914.17785539 ; 2 : -899812481.155632 ; 3 : -40879305.0143522 ; 4 : -1187298049.39919 ; 5 : -25143119.9087468 ; 6 : -430889410.822665 ; 7 : -4669710.06078191 ; 8 : -53924887.6615304 ; 9 : -249560.649671704 ; 10 : -2083856.47599957 ;
Normalized w:
0 : 1 ; 1 : -7152914.17785539 ; 2 : -1272527014.44288 ; 3 : -100133438.324761 ; 4 : -5816548787.25959 ; 5 : -275429078.801557 ; 6 : -11561976160.6118 ; 7 : -331516527.402345 ; 8 : -10828031506.0183 ; 9 : -150334142.238856 ; 10 : -3969623522.48133 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-14-23.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.0666527623858572 ; 2 : -18.8360112512122 ; 3 : 0.477117467186015 ; 4 : -28.861485359655 ; 5 : 0.284559239513281 ; 6 : -11.2479882203183 ; 7 : 0.05364623108289 ; 8 : -1.48182311010333 ; 9 : 0.00302767512853031 ; 10 : -0.0597102447593446 ;
Normalized w:
0 : 1 ; 1 : 0.0666527623858572 ; 2 : -26.6381425724766 ; 3 : 1.16869434197483 ; 4 : -141.391824699924 ; 5 : 3.11719028855879 ; 6 : -301.815195248984 ; 7 : 3.80850459778771 ; 8 : -297.547719028286 ; 9 : 1.82385702242837 ; 10 : -113.744490016337 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-14-24.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -1.13483165329766 ; 2 : -3.14189240521057 ; 3 : -3.85556204061568 ; 4 : -4.81394735425755 ; 5 : -2.35539461777473 ; 6 : -1.86406141067735 ; 7 : -0.436853034827643 ; 8 : -0.246595549989843 ; 9 : -0.0237534508055248 ; 10 : -0.0100330687573344 ;
Normalized w:
0 : 1 ; 1 : -1.13483165329766 ; 2 : -4.44330685096582 ; 3 : -9.44415967115228 ; 4 : -23.5834293331042 ; 5 : -25.8020552796295 ; 6 : -50.0180163421044 ; 7 : -31.0134888903544 ; 8 : -49.5159934554448 ; 9 : -14.3089652024829 ; 10 : -19.1124034694775 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-14-25.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 1.50510433909097 ; 2 : -3.64397245792185 ; 3 : 4.81169521394091 ; 4 : -5.47553289210348 ; 5 : 2.90126212491159 ; 6 : -2.08900027148297 ; 7 : 0.532758762679652 ; 8 : -0.271508175617894 ; 9 : 0.0285383088217531 ; 10 : -0.0108432259294952 ;
Normalized w:
0 : 1 ; 1 : 1.50510433909097 ; 2 : -5.1533552709071 ; 3 : 11.7861980719472 ; 4 : -26.8245233109588 ; 5 : 31.7817342209889 ; 6 : -56.0537593446173 ; 7 : 37.8221201418991 ; 8 : -54.5184089800045 ; 9 : 17.1913407955528 ; 10 : -20.6557050377746 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-14-26.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.345757815160744 ; 2 : -4.37784867134509 ; 3 : 0.983155629773327 ; 4 : -6.70261562851948 ; 5 : 0.582526225317591 ; 6 : -2.69298081052719 ; 7 : 0.104848166218479 ; 8 : -0.367463138049622 ; 9 : 0.00547179228580678 ; 10 : -0.0155521724928187 ;
Normalized w:
0 : 1 ; 1 : 0.345757815160744 ; 2 : -6.19121296503327 ; 3 : 2.4082296306893 ; 4 : -32.8359764637534 ; 5 : 6.38125507889563 ; 6 : -72.2602578532954 ; 7 : 7.44348139752256 ; 8 : -73.786012519414 ; 9 : 3.29618151290307 ; 10 : -29.6259701492 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-14-27.png" width="672" style="display: block; margin: auto;" /></p>
</div>
<div id="lambda-1-2" class="section level3">
<h3><span class="math inline">\(\lambda = 1\)</span></h3>
<pre class="r"><code>CorNullPlot("friendly", L, lambda = 1, rho)</code></pre>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.990193622763482 ; 2 : -5.06198921317001 ; 3 : 3.08726746712871 ; 4 : -6.63454555986282 ; 5 : 1.79513442315682 ; 6 : -2.42359996013425 ; 7 : 0.323704259987644 ; 8 : -0.311160663080113 ; 9 : 0.0170326428239071 ; 10 : -0.0124270992850921 ;
Normalized w:
0 : 1 ; 1 : 0.990193622763482 ; 2 : -7.15873379785134 ; 3 : 7.56222999395997 ; 4 : -32.5025025938233 ; 5 : 19.6647123463403 ; 6 : -65.0320111335117 ; 7 : 22.9807227385935 ; 8 : -62.4805652709523 ; 9 : 10.2603826058368 ; 10 : -23.6728902429088 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-15-1.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -3.12684190211306 ; 2 : -17.6353975654966 ; 3 : -8.46737310674435 ; 4 : -20.254336932018 ; 5 : -4.64802228386959 ; 6 : -6.80704817888075 ; 7 : -0.790739086096404 ; 8 : -0.807908388025388 ; 9 : -0.0397126751314222 ; 10 : -0.029734876458029 ;
Normalized w:
0 : 1 ; 1 : -3.12684190211306 ; 2 : -24.9402184149668 ; 3 : -20.7407435732884 ; 4 : -99.2255811237051 ; 5 : -50.9165330532411 ; 6 : -182.652269449122 ; 7 : -56.1369062515392 ; 8 : -162.226716806982 ; 9 : -23.9227256370203 ; 10 : -56.6431836286852 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-15-2.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -10.7940524339494 ; 2 : -26.247769705336 ; 3 : -28.248298873281 ; 4 : -28.3993929685435 ; 5 : -14.9756538800984 ; 6 : -8.69700899339039 ; 7 : -2.45772441408362 ; 8 : -0.908393242956987 ; 9 : -0.117273938365903 ; 10 : -0.0278007549535556 ;
Normalized w:
0 : 1 ; 1 : -10.7940524339494 ; 2 : -37.1199518993318 ; 3 : -69.1939183411753 ; 4 : -139.128043555432 ; 5 : -164.050068870393 ; 6 : -233.365239721775 ; 7 : -174.481124623085 ; 8 : -182.403915541384 ; 9 : -70.6452597971797 ; 10 : -52.9587963842078 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-15-3.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.331063312897156 ; 2 : -3.1562793110714 ; 3 : -1.19059699958548 ; 4 : -3.87849247704236 ; 5 : -0.689041864478171 ; 6 : -1.46387307310445 ; 7 : -0.125483240535191 ; 8 : -0.191160642893188 ; 9 : -0.0067641794121115 ; 10 : -0.00793607331546585 ;
Normalized w:
0 : 1 ; 1 : -0.331063312897156 ; 2 : -4.46365300835478 ; 3 : -2.91635513827306 ; 4 : -19.000655079954 ; 5 : -7.54807544480224 ; 6 : -39.2798364227168 ; 7 : -8.90842634937685 ; 8 : -38.3847524532686 ; 9 : -4.07470933902129 ; 10 : -15.1177509929509 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-15-4.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.951032913951243 ; 2 : -5.84897758568653 ; 3 : 2.90624068444014 ; 4 : -7.73953612586871 ; 5 : 1.70378526127289 ; 6 : -2.82906893276751 ; 7 : 0.306395914747298 ; 8 : -0.364262701586486 ; 9 : 0.016118466422511 ; 10 : -0.0145937977983201 ;
Normalized w:
0 : 1 ; 1 : 0.951032913951243 ; 2 : -8.27170342769413 ; 3 : 7.1188067465953 ; 4 : -37.9158287084305 ; 5 : 18.6640324148799 ; 6 : -75.9118853604111 ; 7 : 21.7519521223296 ; 8 : -73.1433699779336 ; 9 : 9.70968711221761 ; 10 : -27.8003229539881 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-15-5.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.0249702803783759 ; 2 : -0.145657076906457 ; 3 : -0.0157505623782447 ; 4 : -0.0847934620633242 ; 5 : -4.75765185936808e-05 ; 6 : -0.0371188234915361 ; 7 : -0.000870044588121193 ; 8 : -0.00566998863502667 ; 9 : 2.68712178291464e-05 ; 10 : -0.000297923943091384 ;
Normalized w:
0 : 1 ; 1 : -0.0249702803783759 ; 2 : -0.205990213616732 ; 3 : -0.0385808409885771 ; 4 : -0.415401431158374 ; 5 : -0.000521174648826459 ; 6 : -0.996002550862689 ; 7 : -0.0617670383781483 ; 8 : -1.13852468203904 ; 9 : 0.0161870931517943 ; 10 : -0.567527517382724 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-15-6.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.00196487934640798 ; 2 : -0.0460336617730664 ; 3 : -0.012293675176516 ; 4 : -0.00594223839628071 ; 5 : 0.00365133072737254 ; 6 : 0.00145804112996473 ; 7 : 0.000325135346931134 ; 8 : 1.87667642822963e-05 ; 9 : 7.09738813481104e-05 ; 10 : -3.22422762322365e-07 ;
Normalized w:
0 : 1 ; 1 : -0.00196487934640798 ; 2 : -0.0651014288051664 ; 3 : -0.0301132312459841 ; 4 : -0.0291109040017239 ; 5 : 0.0399983240858737 ; 6 : 0.039123348967101 ; 7 : 0.0230823198330043 ; 8 : 0.00376833636057234 ; 9 : 0.0427543268053942 ; 10 : -0.000614196321214654 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-15-7.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.174535157389586 ; 2 : -1.31940719334627 ; 3 : 0.608000101526193 ; 4 : -1.69157445372129 ; 5 : 0.355179353621336 ; 6 : -0.653402655127321 ; 7 : 0.0662604334520652 ; 8 : -0.0887948633866882 ; 9 : 0.00369286851125707 ; 10 : -0.0038219020120779 ;
Normalized w:
0 : 1 ; 1 : 0.174535157389586 ; 2 : -1.86592354712292 ; 3 : 1.48929001229954 ; 4 : -8.28698854708872 ; 5 : 3.8907948787702 ; 6 : -17.5326330425225 ; 7 : 4.70402412918216 ; 8 : -17.8298670617271 ; 9 : 2.22456633596294 ; 10 : -7.28049762663516 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-15-8.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.010384245552025 ; 2 : -0.122495494717022 ; 3 : -0.00452512868369771 ; 4 : 0.00477788548918738 ; 5 : -0.00662659651902575 ; 6 : -0.0018962703120297 ; 7 : -0.00136806854923071 ; 8 : -0.000301367963661958 ; 9 : -0.000152455470711193 ; 10 : -1.04691243707978e-05 ;
Normalized w:
0 : 1 ; 1 : 0.010384245552025 ; 2 : -0.173234789958415 ; 3 : -0.0110842562954915 ; 4 : 0.0234067629959142 ; 5 : -0.0725907278591123 ; 6 : -0.0508822718569577 ; 7 : -0.0971232322319784 ; 8 : -0.0605142068337442 ; 9 : -0.0918384466827538 ; 10 : -0.0199430636614102 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-15-9.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -54.4330577997137 ; 2 : -75.3822582526047 ; 3 : -127.859373985824 ; 4 : -70.8745891606404 ; 5 : -62.1956911684788 ; 6 : -16.804005937536 ; 7 : -9.32467943951548 ; 8 : -1.05535708335353 ; 9 : -0.402535746802676 ; 10 : 1.2533478632639e-16 ;
Normalized w:
0 : 1 ; 1 : -54.4330577997137 ; 2 : -106.606611983145 ; 3 : -313.190225096953 ; 4 : -347.213158345921 ; 5 : -681.319660652013 ; 6 : -450.898794847688 ; 7 : -661.986570192026 ; 8 : -211.914020486758 ; 9 : -242.485609392606 ; 10 : 2.38755366176433e-13 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-15-10.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 18.2167132280335 ; 2 : -37.2481635623401 ; 3 : 46.1255530784785 ; 4 : -38.2497706023594 ; 5 : 23.4756614518062 ; 6 : -10.7758172978181 ; 7 : 3.67072070506425 ; 8 : -0.98639919204478 ; 9 : 0.165296958584317 ; 10 : -0.0231442798200358 ;
Normalized w:
0 : 1 ; 1 : 18.2167132280335 ; 2 : -52.6768580833527 ; 3 : 112.984069145934 ; 4 : -187.384841508578 ; 5 : 257.162986590174 ; 6 : -289.145519892473 ; 7 : 260.595318631629 ; 8 : -198.06738580545 ; 9 : 99.574097583713 ; 10 : -44.088486247804 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-15-11.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -7.17853175053795 ; 2 : -27.0506794832733 ; 3 : -18.2475960181493 ; 4 : -28.2131254788656 ; 5 : -9.6095878910105 ; 6 : -8.77280537330281 ; 7 : -1.55284600963663 ; 8 : -0.942375623132412 ; 9 : -0.0735891904070297 ; 10 : -0.0306917638899097 ;
Normalized w:
0 : 1 ; 1 : -7.17853175053795 ; 2 : -38.2554377966527 ; 3 : -44.6972992769079 ; 4 : -138.215522944672 ; 5 : -105.267761124699 ; 6 : -235.399070016966 ; 7 : -110.241130606538 ; 8 : -189.227523325207 ; 9 : -44.329776478968 ; 10 : -58.4659976764417 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-15-12.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.221054473926752 ; 2 : -1.43221033522857 ; 3 : -0.750033598456729 ; 4 : -1.98498166157922 ; 5 : -0.452597605035338 ; 6 : -0.760018870400118 ; 7 : -0.0860219012244282 ; 8 : -0.103249684371707 ; 9 : -0.00468799688277602 ; 10 : -0.00443544626823974 ;
Normalized w:
0 : 1 ; 1 : -0.221054473926752 ; 2 : -2.02545128025117 ; 3 : -1.83719960616251 ; 4 : -9.72438443930199 ; 5 : -4.95795835501337 ; 6 : -20.3934463007672 ; 7 : -6.10694916885158 ; 8 : -20.7323720798561 ; 9 : -2.82402690936123 ; 10 : -8.44926320113332 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-15-13.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 1.19624893178564 ; 2 : -2.78874517700335 ; 3 : 3.62922444518989 ; 4 : -3.54630222772657 ; 5 : 2.14075870122612 ; 6 : -1.2352662665503 ; 7 : 0.386386406860824 ; 8 : -0.148139424670228 ; 9 : 0.0208324224662385 ; 10 : -0.0052923077513501 ;
Normalized w:
0 : 1 ; 1 : 1.19624893178564 ; 2 : -3.9438812513207 ; 3 : 8.88974805275061 ; 4 : -17.3732618632507 ; 5 : 23.4508366167402 ; 6 : -33.1456721078263 ; 7 : 27.4307137211259 ; 8 : -29.7461603940805 ; 9 : 12.549351696028 ; 10 : -10.0815337236181 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-15-14.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 173.100946298253 ; 2 : -132.056233792338 ; 3 : 346.270132417169 ; 4 : -96.7141880167721 ; 5 : 152.034197990412 ; 6 : -15.6177233256506 ; 7 : 21.0879731371861 ; 8 : -1.17392349241305e-13 ; 9 : 0.852421119433525 ; 10 : 0.0632963828889122 ;
Normalized w:
0 : 1 ; 1 : 173.100946298253 ; 2 : -186.755716825037 ; 3 : 848.185137588027 ; 4 : -473.800823057374 ; 5 : 1665.45119503111 ; 6 : -419.067492119265 ; 7 : 1497.09757852145 ; 8 : -2.35721966474706e-11 ; 9 : 513.494407010491 ; 10 : 120.57587137007 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-15-15.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 5.3495265524959 ; 2 : -14.9487809688657 ; 3 : 14.7915257998395 ; 4 : -17.516684025336 ; 5 : 8.30244894568615 ; 6 : -5.8646959351151 ; 7 : 1.41827520328496 ; 8 : -0.674850522217663 ; 9 : 0.0713638273861906 ; 10 : -0.0236897651229084 ;
Normalized w:
0 : 1 ; 1 : 5.3495265524959 ; 2 : -21.1407687871147 ; 3 : 36.2316907268197 ; 4 : -85.813875695269 ; 5 : 90.9487714017457 ; 6 : -157.366305339409 ; 7 : 100.687551084308 ; 8 : -135.50890939804 ; 9 : 42.9892284344425 ; 10 : -45.1276035355778 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-15-16.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.00977765933816548 ; 2 : -0.145932485463695 ; 3 : -0.0113791478754545 ; 4 : 0.0112463330904812 ; 5 : -0.000710737922922955 ; 6 : -0.000368517744149794 ; 7 : -0.000430361315273652 ; 8 : -6.51178268932423e-05 ; 9 : -3.72003634967045e-05 ; 10 : 8.81824604196897e-10 ;
Normalized w:
0 : 1 ; 1 : 0.00977765933816548 ; 2 : -0.206379700133572 ; 3 : -0.0278731060025389 ; 4 : 0.0550955550981134 ; 5 : -0.00778574385718541 ; 6 : -0.00988836872200579 ; 7 : -0.0305526225206233 ; 8 : -0.013075555866322 ; 9 : -0.0224093211193656 ; 10 : 1.67982379393173e-06 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-15-17.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.0384872560271654 ; 2 : -20.0257032861721 ; 3 : 0.113946543302254 ; 4 : -22.2940309104237 ; 5 : 0.0899959890306396 ; 6 : -7.39771516628133 ; 7 : 0.0159779049132858 ; 8 : -0.863265886010817 ; 9 : 0.00077959307039399 ; 10 : -0.0312699095652114 ;
Normalized w:
0 : 1 ; 1 : 0.0384872560271654 ; 2 : -28.320621183364 ; 3 : 0.27911088904447 ; 4 : -109.218000080748 ; 5 : 0.985856665541376 ; 6 : -198.501527879835 ; 7 : 1.13431872280534 ; 8 : -173.342414182985 ; 9 : 0.469623138452364 ; 10 : -59.5673310449011 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-15-18.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.0424900126823913 ; 2 : -0.204862447943877 ; 3 : 0.00823062156162634 ; 4 : 0.0242143926329621 ; 5 : 0.00461118704563706 ; 6 : -0.00302938347417584 ; 7 : 0.00123143806005101 ; 8 : -5.90971996918201e-08 ; 9 : 0.000112710544350614 ; 10 : -1.61792155923727e-05 ;
Normalized w:
0 : 1 ; 1 : -0.0424900126823913 ; 2 : -0.289719252303183 ; 3 : 0.0201608230919338 ; 4 : 0.11862581276433 ; 5 : 0.0505130232354205 ; 6 : -0.0812868885380598 ; 7 : 0.0874234297344866 ; 8 : -1.18666235189395e-05 ; 9 : 0.0678962930594794 ; 10 : -0.030820450223172 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-15-19.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.930400264415246 ; 2 : -3.70186603891747 ; 3 : 2.85944248854643 ; 4 : -4.60728914576893 ; 5 : 1.683640400931 ; 6 : -1.69847916780134 ; 7 : 0.303804292845106 ; 8 : -0.215579216554214 ; 9 : 0.0162110032605313 ; 10 : -0.00859144761394906 ;
Normalized w:
0 : 1 ; 1 : 0.930400264415246 ; 2 : -5.23522915832545 ; 3 : 7.00417504577288 ; 4 : -22.5710150091945 ; 5 : 18.443356526339 ; 6 : -45.5749785308527 ; 7 : 21.5679652190377 ; 8 : -43.2879631301865 ; 9 : 9.76543086103208 ; 10 : -16.3662003277549 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-15-20.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.189357436074152 ; 2 : -2.18713998400049 ; 3 : 0.523457390283247 ; 4 : -2.73704853728455 ; 5 : 0.314494381158206 ; 6 : -1.05126845117824 ; 7 : 0.0578881914886824 ; 8 : -0.139964604172638 ; 9 : 0.00313233378949845 ; 10 : -0.00591258914801345 ;
Normalized w:
0 : 1 ; 1 : 0.189357436074152 ; 2 : -3.09308302818197 ; 3 : 1.28220350828286 ; 4 : -13.4087446351564 ; 5 : 3.44511333537955 ; 6 : -28.2084926332256 ; 7 : 4.10965391215672 ; 8 : -28.1046694658186 ; 9 : 1.88690289943346 ; 10 : -11.2631331529029 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-15-21.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -5.29085254945192 ; 2 : -14.3122890576611 ; 3 : -14.7633316610083 ; 4 : -17.2110730605033 ; 5 : -8.31779378885616 ; 6 : -5.77119243820943 ; 7 : -1.43202147996183 ; 8 : -0.668110253268745 ; 9 : -0.0720887000158238 ; 10 : -0.0235738734129143 ;
Normalized w:
0 : 1 ; 1 : -5.29085254945192 ; 2 : -20.2406332939483 ; 3 : -36.162629472946 ; 4 : -84.3166938479896 ; 5 : -91.1168657366576 ; 6 : -154.857343236828 ; 7 : -101.663439918799 ; 8 : -134.155474134604 ; 9 : -43.4258882409932 ; 10 : -44.9068366721439 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-15-22.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.011031824614049 ; 2 : -8.51372794977676 ; 3 : -0.410722731336789 ; 4 : -10.715802734123 ; 5 : -0.232420664177928 ; 6 : -3.89870034133524 ; 7 : -0.0444726298975924 ; 8 : -0.496342841465798 ; 9 : -0.00247893408959616 ; 10 : -0.0198482864164879 ;
Normalized w:
0 : 1 ; 1 : -0.011031824614049 ; 2 : -12.0402295329292 ; 3 : -1.00606111753736 ; 4 : -52.4964977658445 ; 5 : -2.54604081201168 ; 6 : -104.613107845527 ; 7 : -3.15724351966102 ; 8 : -99.6648515785855 ; 9 : -1.49329804404798 ; 10 : -37.809813462342 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-15-23.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.0666353041034338 ; 2 : -1.60032561962479 ; 3 : 0.0517533578936664 ; 4 : -2.07037521903444 ; 5 : 0.0166280812133002 ; 6 : -0.800999203808154 ; 7 : 0.00365296790993558 ; 8 : -0.109256481675998 ; 9 : 0.000232838623536709 ; 10 : -0.00472374471145179 ;
Normalized w:
0 : 1 ; 1 : -0.0666353041034338 ; 2 : -2.26320219548651 ; 3 : 0.126769319315123 ; 4 : -10.1427257254747 ; 5 : 0.182151503371048 ; 6 : -21.4930640356589 ; 7 : 0.259334995203378 ; 8 : -21.9385274059344 ; 9 : 0.140260873641394 ; 10 : -8.99845470968976 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-15-24.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.188237567641041 ; 2 : -0.727450065306265 ; 3 : -0.827449304863473 ; 4 : -0.996064881386437 ; 5 : -0.518184044043969 ; 6 : -0.368364827100734 ; 7 : -0.0996552594120817 ; 8 : -0.0489492642681959 ; 9 : -0.00588586410791703 ; 10 : -0.00200580461455446 ;
Normalized w:
0 : 1 ; 1 : -0.188237567641041 ; 2 : -1.02876974830531 ; 3 : -2.02682858493615 ; 4 : -4.87970142020524 ; 5 : -5.67642179724264 ; 6 : -9.88426552700637 ; 7 : -7.07482158584837 ; 8 : -9.82893425794854 ; 9 : -3.54561639890819 ; 10 : -3.82093933586174 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-15-25.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.318575961780774 ; 2 : -0.860139438027326 ; 3 : 1.03590672218289 ; 4 : -1.13605981347938 ; 5 : 0.637587012294198 ; 6 : -0.413538763943057 ; 7 : 0.122934836233099 ; 8 : -0.0531536223784576 ; 9 : 0.00710771583295954 ; 10 : -0.00209124180424253 ;
Normalized w:
0 : 1 ; 1 : 0.318575961780774 ; 2 : -1.21642085879022 ; 3 : 2.53744289046714 ; 4 : -5.56553372061184 ; 5 : 6.98441578011712 ; 6 : -11.096409450095 ; 7 : 8.72750759132757 ; 8 : -10.6731626662902 ; 9 : 4.28165403652843 ; 10 : -3.98369213663598 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-15-26.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.0620172351956328 ; 2 : -0.589578226923912 ; 3 : 0.113546479302921 ; 4 : -0.633477934320979 ; 5 : 0.0701074140159413 ; 6 : -0.254175761793915 ; 7 : 0.0137122611200663 ; 8 : -0.0357105237849158 ; 9 : 0.000780670980072819 ; 10 : -0.00161871095325211 ;
Normalized w:
0 : 1 ; 1 : 0.0620172351956328 ; 2 : -0.833789524595679 ; 3 : 0.278130936381648 ; 4 : -3.10339540479743 ; 5 : 0.767988242097698 ; 6 : -6.82025137924784 ; 7 : 0.973473969516084 ; 8 : -7.170616266584 ; 9 : 0.470272466089517 ; 10 : -3.083548771297 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-15-27.png" width="672" style="display: block; margin: auto;" /></p>
</div>
<div id="lambda-10-2" class="section level3">
<h3><span class="math inline">\(\lambda = 10\)</span></h3>
<pre class="r"><code>CorNullPlot("friendly", L, lambda = 10, rho)</code></pre>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.0195328556153761 ; 2 : -0.0594702211988415 ; 3 : 0.0327668711521069 ; 4 : -0.0169877651859634 ; 5 : 0.00795464094593129 ; 6 : -2.07582093003884e-11 ; 7 : 0.00224884250417521 ; 8 : -0.000339881382700872 ; 9 : 0.000129544930260427 ; 10 : 4.48933975887091e-13 ;
Normalized w:
0 : 1 ; 1 : -0.0195328556153761 ; 2 : -0.0841035933767297 ; 3 : 0.080262114790184 ; 4 : -0.0832227131516528 ; 5 : 0.087138725658816 ; 6 : -5.57001205042042e-10 ; 7 : 0.159651980091913 ; 8 : -0.068247640000548 ; 9 : 0.0780372466481116 ; 10 : 8.55192711804991e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-16-1.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.0358065026199347 ; 2 : -0.109813620241973 ; 3 : -0.0921611131009101 ; 4 : -0.00449357364221964 ; 5 : -0.0504514864252425 ; 6 : -1.94204096867876e-08 ; 7 : -0.0093778326270938 ; 8 : -8.94253451505833e-05 ; 9 : -0.0006100283237745 ; 10 : 9.25920346995506e-06 ;
Normalized w:
0 : 1 ; 1 : -0.0358065026199347 ; 2 : -0.155299911079488 ; 3 : -0.22574770122416 ; 4 : -0.0220139250901157 ; 5 : -0.55266834349542 ; 6 : -5.21104274526629e-07 ; 7 : -0.665760072173299 ; 8 : -0.0179564667951614 ; 9 : -0.367478145760112 ; 10 : 0.0176382357984341 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-16-2.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.0460601509345883 ; 2 : -0.126969252938243 ; 3 : -0.106549961827225 ; 4 : -0.00238883209912362 ; 5 : -0.0419417937955603 ; 6 : -0.00035906754302965 ; 7 : -0.00862519569198984 ; 8 : -1.54466744023286e-10 ; 9 : -0.000393557258811038 ; 10 : 3.5719540097369e-06 ;
Normalized w:
0 : 1 ; 1 : -0.0460601509345883 ; 2 : -0.179561639509643 ; 3 : -0.260993038589726 ; 4 : -0.0117028394480691 ; 5 : -0.459449331281172 ; 6 : -0.00963479321673753 ; 7 : -0.612328150303908 ; 8 : -3.10166760367572e-08 ; 9 : -0.237077011151655 ; 10 : 0.00680436144311315 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-16-3.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.052220166264115 ; 2 : -0.21578873505685 ; 3 : -0.0244235984878817 ; 4 : 0.0211278222084139 ; 5 : -1.9126721069789e-05 ; 6 : -0.00287676898704295 ; 7 : -0.000720157379246019 ; 8 : -1.47354411958072e-09 ; 9 : -1.17986761712105e-05 ; 10 : 1.67359379171181e-11 ;
Normalized w:
0 : 1 ; 1 : 0.052220166264115 ; 2 : -0.305171355724732 ; 3 : -0.0598253539779209 ; 4 : 0.103504767573713 ; 5 : -0.000209522731620656 ; 6 : -0.077191812127095 ; 7 : -0.0511261021440885 ; 8 : -2.95885310925008e-07 ; 9 : -0.00710746611729978 ; 10 : 3.18809733739997e-08 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-16-4.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.0197859117021518 ; 2 : -0.00406558148012681 ; 3 : 0.0104864413529932 ; 4 : -0.0241463436813757 ; 5 : 0.0095341067489564 ; 6 : -2.30755579411994e-08 ; 7 : 0.00132100603554299 ; 8 : -0.000272497380541538 ; 9 : 8.72209435131181e-05 ; 10 : -1.68394832766551e-11 ;
Normalized w:
0 : 1 ; 1 : -0.0197859117021518 ; 2 : -0.00574960046812822 ; 3 : 0.0256864305324541 ; 4 : -0.118292442346494 ; 5 : 0.104440906641313 ; 6 : -6.19182194103084e-07 ; 7 : 0.0937821252027416 ; 8 : -0.0547170397522438 ; 9 : 0.052541479378089 ; 10 : -3.20782211689395e-08 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-16-5.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.0218574539676484 ; 2 : -0.0824037408603593 ; 3 : -0.00614002807237893 ; 4 : 0.00211489988953475 ; 5 : 0.00698604161515864 ; 6 : -2.35189922485386e-07 ; 7 : 0.000594880543450452 ; 8 : -1.74727509540128e-11 ; 9 : 0.000114857534915558 ; 10 : -1.99581782474016e-12 ;
Normalized w:
0 : 1 ; 1 : -0.0218574539676484 ; 2 : -0.116536487914998 ; 3 : -0.015039935783693 ; 4 : 0.0103608511728573 ; 5 : 0.0765282516058443 ; 6 : -6.31080785160275e-06 ; 7 : 0.0422323290775984 ; 8 : -3.50850054643384e-09 ; 9 : 0.0691896299112644 ; 10 : -3.8019150910457e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-16-6.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.00237432331769622 ; 2 : -0.0462398949391692 ; 3 : -0.0124993074733049 ; 4 : -0.00552754002397608 ; 5 : 0.00393970330098859 ; 6 : 0.00118301483874229 ; 7 : 0.000429658426868888 ; 8 : 2.74361575907938e-11 ; 9 : 7.80029473540958e-05 ; 10 : -7.39434057412163e-12 ;
Normalized w:
0 : 1 ; 1 : -0.00237432331769622 ; 2 : -0.0653930865456801 ; 3 : -0.0306169254477536 ; 4 : -0.0270793051831058 ; 5 : 0.0431572873565804 ; 6 : 0.0317436191738246 ; 7 : 0.030502722394049 ; 8 : 5.50913672109759e-09 ; 9 : 0.04698860256217 ; 10 : -1.40857821132771e-08 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-16-7.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.0219431041356869 ; 2 : -0.0876866619950901 ; 3 : 0.0103921746392133 ; 4 : 0.00287985137303969 ; 5 : -0.00286862935053328 ; 6 : -1.43079259662589e-08 ; 7 : -0.000390282821116643 ; 8 : -5.56132021440079e-10 ; 9 : -3.40538734311794e-05 ; 10 : -1.77299089694446e-12 ;
Normalized w:
0 : 1 ; 1 : -0.0219431041356869 ; 2 : -0.124007666632682 ; 3 : 0.0254555251839644 ; 4 : 0.0141083327980016 ; 5 : -0.0314242600881694 ; 6 : -3.8392194093107e-07 ; 7 : -0.027707331692391 ; 8 : -1.11670423635481e-07 ; 9 : -0.0205138905469334 ; 10 : -3.37744295286939e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-16-8.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.0102699849664691 ; 2 : -0.118163058545407 ; 3 : -0.00428146303544641 ; 4 : 0.00897886931340816 ; 5 : -0.00607702256265007 ; 6 : -2.18022463958924e-08 ; 7 : -0.00118125633382797 ; 8 : -6.11416895527969e-11 ; 9 : -0.000134049780259931 ; 10 : 1.00710494016409e-12 ;
Normalized w:
0 : 1 ; 1 : 0.0102699849664691 ; 2 : -0.1671077999664 ; 3 : -0.0104873997894313 ; 4 : 0.0439872965699679 ; 5 : -0.0665704468006259 ; 6 : -5.85015660040982e-07 ; 7 : -0.0838608805826161 ; 8 : -1.22771538248595e-08 ; 9 : -0.0807509467505956 ; 10 : 1.91847543538952e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-16-9.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.690852916751373 ; 2 : -0.770513800087517 ; 3 : -1.5951688203757 ; 4 : -0.476494992189659 ; 5 : -0.778618867408852 ; 6 : -0.0880627775922175 ; 7 : -0.123013457323572 ; 8 : -2.33870595579938e-09 ; 9 : -0.0057429502369907 ; 10 : 0.000532638661057973 ;
Normalized w:
0 : 1 ; 1 : -0.690852916751373 ; 2 : -1.0896710660794 ; 3 : -3.90734966351781 ; 4 : -2.33433919171224 ; 5 : -8.52934234757905 ; 6 : -2.36297228380372 ; 7 : -8.73308913505404 ; 8 : -4.69608428888282e-07 ; 9 : -3.45952576631845 ; 10 : 1.01464519378883 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-16-10.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.108170384139922 ; 2 : -0.206147375474361 ; 3 : 0.348130623086922 ; 4 : -0.0689149401615465 ; 5 : 0.168482070248735 ; 6 : -0.012301961557552 ; 7 : 0.0290133584820416 ; 8 : -2.05835313635092e-11 ; 9 : 0.00150964681283809 ; 10 : 0.000108494336084961 ;
Normalized w:
0 : 1 ; 1 : 0.108170384139922 ; 2 : -0.29153641424346 ; 3 : 0.852742390400132 ; 4 : -0.337612878100449 ; 5 : 1.84562860820805 ; 6 : -0.330096267591305 ; 7 : 2.05974412266513 ; 8 : -4.13314029522206e-09 ; 9 : 0.909404022590064 ; 10 : 0.206675302996705 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-16-11.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.0637215144298066 ; 2 : -0.262073035099418 ; 3 : -0.117674346743829 ; 4 : -1.31362021474771e-08 ; 5 : -0.0677801757615273 ; 6 : -0.00976843860254607 ; 7 : -0.0113770055593337 ; 8 : -0.000159614148663148 ; 9 : -0.000668956679339544 ; 10 : 1.55414115533463e-14 ;
Normalized w:
0 : 1 ; 1 : -0.0637215144298066 ; 2 : -0.370627240569877 ; 3 : -0.288242105337721 ; 4 : -6.4353984838743e-08 ; 5 : -0.742494624325068 ; 6 : -0.262114712991913 ; 7 : -0.807687270981434 ; 8 : -0.0320502666853735 ; 9 : -0.402976305422186 ; 10 : 2.96054711950034e-11 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-16-12.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.0204714511128345 ; 2 : -0.0019488370924672 ; 3 : -0.00517120655273784 ; 4 : -0.0115228121135017 ; 5 : 0.00619618674533238 ; 6 : -0.000185925539428495 ; 7 : 0.000897022879882511 ; 8 : -2.25200579835849e-12 ; 9 : 0.000144329328823017 ; 10 : -2.09476166451391e-13 ;
Normalized w:
0 : 1 ; 1 : 0.0204714511128345 ; 2 : -0.00275607184702286 ; 3 : -0.0126668174087445 ; 4 : -0.0564500201600805 ; 5 : 0.0678758250186613 ; 6 : -0.00498890573898519 ; 7 : 0.0636823070958086 ; 8 : -4.52199175442281e-10 ; 9 : 0.0869432976595516 ; 10 : -3.99039726258398e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-16-13.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.0121335548047993 ; 2 : -0.0663113142773513 ; 3 : 0.0687073217928708 ; 4 : -0.0161256952537096 ; 5 : 0.0495645889278382 ; 6 : -6.25991565418021e-11 ; 7 : 0.00810031746570205 ; 8 : -0.000443511317927794 ; 9 : 0.000584817950651624 ; 10 : 7.69983331647635e-06 ;
Normalized w:
0 : 1 ; 1 : 0.0121335548047993 ; 2 : -0.0937783599898149 ; 3 : 0.16829787998574 ; 4 : -0.0789994502384182 ; 5 : 0.542952868184955 ; 6 : -1.67971163233944e-09 ; 7 : 0.575065492746343 ; 8 : -0.0890563658461515 ; 9 : 0.35229153751905 ; 10 : 0.0146677277462732 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-16-14.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 10.2719823637698 ; 2 : -7.20318460817093 ; 3 : 20.5304480391493 ; 4 : -5.14993400932367 ; 5 : 9.07432025323978 ; 6 : -0.832396689612991 ; 7 : 1.27984170747343 ; 8 : -2.59643563638919e-13 ; 9 : 0.0529876608783972 ; 10 : 0.00336478860889876 ;
Normalized w:
0 : 1 ; 1 : 10.2719823637698 ; 2 : -10.1868413651525 ; 3 : 50.2891218866391 ; 4 : -25.2294210636972 ; 5 : 99.4041979345084 ; 6 : -22.3355469866453 ; 7 : 90.859747813815 ; 8 : -5.21360138024495e-11 ; 9 : 31.9195135846789 ; 10 : 6.40972358888335 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-16-15.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.0804250190946633 ; 2 : -0.20913154981791 ; 3 : 0.103270453174378 ; 4 : 3.84587195093193e-09 ; 5 : 0.0748879788157968 ; 6 : -0.00542799485448755 ; 7 : 0.012861860087431 ; 8 : -0.000338450326123986 ; 9 : 0.000885476047793812 ; 10 : 6.65904652059143e-11 ;
Normalized w:
0 : 1 ; 1 : 0.0804250190946633 ; 2 : -0.295756674072593 ; 3 : 0.252959915783209 ; 4 : 1.88408477917306e-08 ; 5 : 0.820356705667619 ; 6 : -0.145648385713839 ; 7 : 0.913101485235675 ; 8 : -0.0679602861204866 ; 9 : 0.53340653782257 ; 10 : 1.26850903648523e-07 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-16-16.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.00966818161582002 ; 2 : -0.144352607254812 ; 3 : -0.0107263199007162 ; 4 : 0.0118047643901818 ; 5 : -4.37703199769233e-05 ; 6 : -1.41492575058493e-06 ; 7 : -0.000264633093185441 ; 8 : -2.56939343985045e-09 ; 9 : -1.84313786140173e-05 ; 10 : 1.04972765882325e-10 ;
Normalized w:
0 : 1 ; 1 : 0.00966818161582002 ; 2 : -0.204145414943672 ; 3 : -0.0262740105746155 ; 4 : 0.057831298579445 ; 5 : -0.000479479832011598 ; 6 : -3.79664419370737e-05 ; 7 : -0.018787085910402 ; 8 : -5.15930108054822e-07 ; 9 : -0.0111029743585896 ; 10 : 1.9996691973065e-07 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-16-17.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.00447501157548617 ; 2 : -0.167572985101847 ; 3 : 0.0132150369856437 ; 4 : -2.32228572015251e-09 ; 5 : 0.0122440938412845 ; 6 : -0.00467197615102844 ; 7 : 0.00164054685429511 ; 8 : -7.7293018796906e-05 ; 9 : 6.07882820999004e-05 ; 10 : 4.78949215975624e-13 ;
Normalized w:
0 : 1 ; 1 : 0.00447501157548617 ; 2 : -0.236983988218376 ; 3 : 0.0323700975468345 ; 4 : -1.13768301026509e-08 ; 5 : 0.134127327861632 ; 6 : -0.125362275155489 ; 7 : 0.116467272935076 ; 8 : -0.0155203149978044 ; 9 : 0.0366185705145578 ; 10 : 9.12369971592623e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-16-18.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.0434220236573529 ; 2 : -0.200385262367952 ; 3 : 0.0103381531632292 ; 4 : 0.0227892305136963 ; 5 : 0.00696555414161558 ; 6 : -0.00265351698638848 ; 7 : 0.00189670056127292 ; 8 : 3.18781806534009e-09 ; 9 : 0.000165032100099215 ; 10 : -4.78218419472237e-11 ;
Normalized w:
0 : 1 ; 1 : -0.0434220236573529 ; 2 : -0.283387555740449 ; 3 : 0.0253232001326513 ; 4 : 0.111643972778441 ; 5 : 0.0763038225777278 ; 6 : -0.0712013323321804 ; 7 : 0.134652382141685 ; 8 : 6.40108787311978e-07 ; 9 : 0.0994145480985482 ; 10 : -9.10977847411613e-08 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-16-19.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.00291477779865538 ; 2 : -0.194376806506933 ; 3 : 0.0431939408090762 ; 4 : 0.0168149612240841 ; 5 : 0.0197021958887266 ; 6 : -0.00330098871309094 ; 7 : 0.00401295902122041 ; 8 : -1.55454575419173e-11 ; 9 : 0.000247924354977249 ; 10 : -1.48433368797897e-13 ;
Normalized w:
0 : 1 ; 1 : 0.00291477779865538 ; 2 : -0.274890315972875 ; 3 : 0.105803114962216 ; 4 : 0.0823761500873819 ; 5 : 0.215826742412822 ; 6 : -0.0885748218651706 ; 7 : 0.284891828830192 ; 8 : -3.12150310068116e-09 ; 9 : 0.14934844613787 ; 10 : -2.82756801673994e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-16-20.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.0224977140060591 ; 2 : -0.158381286470429 ; 3 : 0.0127132227896865 ; 4 : 0.013098081242688 ; 5 : 0.00569201257749691 ; 6 : -0.00245792671521922 ; 7 : 0.00139279701419496 ; 8 : -2.66567369529955e-10 ; 9 : 9.76562903258117e-05 ; 10 : 6.46192629315638e-12 ;
Normalized w:
0 : 1 ; 1 : 0.0224977140060591 ; 2 : -0.223984963352579 ; 3 : 0.0311409088210544 ; 4 : 0.0641672313082098 ; 5 : 0.0623528737259636 ; 6 : -0.0659530946273154 ; 7 : 0.0988787790916838 ; 8 : -5.35263029913721e-08 ; 9 : 0.0588276824077534 ; 10 : 1.23095879727273e-08 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-16-21.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.0471633256581118 ; 2 : -0.0580469017988411 ; 3 : -0.065202196387677 ; 4 : -0.00992353133348181 ; 5 : -0.0468154044704704 ; 6 : -0.000377171005801114 ; 7 : -0.00749811376477714 ; 8 : -3.86046041338126e-10 ; 9 : -0.000452502905774796 ; 10 : 1.24095567127934e-10 ;
Normalized w:
0 : 1 ; 1 : -0.0471633256581118 ; 2 : -0.0820907157776602 ; 3 : -0.159712111258549 ; 4 : -0.0486151764271023 ; 5 : -0.512837061344097 ; 6 : -0.0101205600973591 ; 7 : -0.532313271062148 ; 8 : -7.75174298854396e-08 ; 9 : -0.272585587069647 ; 10 : 2.36394726786745e-07 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-16-22.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.0565341807814713 ; 2 : -0.110894994292429 ; 3 : -0.025953693174393 ; 4 : 0.00036040577475903 ; 5 : 0.000968086367006428 ; 6 : -0.00342344857240058 ; 7 : -0.000682305062755083 ; 8 : -2.93638345418113e-12 ; 9 : -2.94916183019017e-05 ; 10 : -2.33817712705689e-13 ;
Normalized w:
0 : 1 ; 1 : 0.0565341807814713 ; 2 : -0.15682920492764 ; 3 : -0.0635733052180175 ; 4 : 0.00176562049702414 ; 5 : 0.0106048548164529 ; 6 : -0.0918607647043476 ; 7 : -0.0484388542520623 ; 8 : -5.89621118085457e-10 ; 9 : -0.0177656098687214 ; 10 : -4.45408934357664e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-16-23.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.077141970314195 ; 2 : -0.0941861763202096 ; 3 : 0.00518987912704219 ; 4 : 0.00177463673695511 ; 5 : -0.01003843133676 ; 6 : -1.73298544241002e-08 ; 7 : -0.00158454069673423 ; 8 : -4.51728148651004e-05 ; 9 : -0.000121666159524278 ; 10 : -6.0880774132438e-13 ;
Normalized w:
0 : 1 ; 1 : -0.077141970314195 ; 2 : -0.133199367940104 ; 3 : 0.0127125556879744 ; 4 : 0.00869390896867551 ; 5 : -0.109965505702203 ; 6 : -4.65008790389564e-07 ; 7 : -0.112491230177376 ; 8 : -0.00907062923607692 ; 9 : -0.0732911128242349 ; 10 : -1.15974279345258e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-16-24.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.0741245213820646 ; 2 : -0.0114951117333178 ; 3 : -0.0117838281938442 ; 4 : -0.0199818298544024 ; 5 : -0.0147475947233081 ; 6 : -1.50088466727849e-10 ; 7 : -0.00208966218713219 ; 8 : -0.000109361186096124 ; 9 : -0.000215171106929808 ; 10 : 7.72261250350425e-14 ;
Normalized w:
0 : 1 ; 1 : 0.0741245213820646 ; 2 : -0.0162565429142521 ; 3 : -0.0288643662915406 ; 4 : -0.0978905745407946 ; 5 : -0.161551805978 ; 6 : -4.02729617090624e-09 ; 7 : -0.148351298625606 ; 8 : -0.0219595518866355 ; 9 : -0.129618046103947 ; 10 : 1.47111207523129e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-16-25.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.0127087577771728 ; 2 : -0.0307315829632796 ; 3 : 0.066735541246966 ; 4 : -0.0139685311010714 ; 5 : 0.0392617512938869 ; 6 : -1.02058089003322e-09 ; 7 : 0.00796781584094096 ; 8 : -3.71711478127709e-05 ; 9 : 0.000489681534400756 ; 10 : -6.19255410939076e-13 ;
Normalized w:
0 : 1 ; 1 : 0.0127087577771728 ; 2 : -0.043461021419864 ; 3 : 0.163468023763527 ; 4 : -0.0684315473076443 ; 5 : 0.43009093661639 ; 6 : -2.73850589598182e-08 ; 7 : 0.56565881054462 ; 8 : -0.00746390724368038 ; 9 : 0.294981815206788 ; 10 : -1.17964498707065e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-16-26.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.0218432423462418 ; 2 : -0.127406783722892 ; 3 : -0.00276965061268409 ; 4 : 0.00721483372468209 ; 5 : -0.00208423119359559 ; 6 : -1.46629812973078e-05 ; 7 : -0.00031832663788253 ; 8 : -2.86524629670372e-11 ; 9 : -4.75723339730603e-05 ; 10 : -4.25023139317261e-12 ;
Normalized w:
0 : 1 ; 1 : 0.0218432423462418 ; 2 : -0.180180401479249 ; 3 : -0.00678423076686282 ; 4 : 0.0353453224089898 ; 5 : -0.0228316087957645 ; 6 : -0.00039344907520306 ; 7 : -0.0225989494415869 ; 8 : -5.75336890230431e-09 ; 9 : -0.0286573465470158 ; 10 : -8.09643980218632e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-16-27.png" width="672" style="display: block; margin: auto;" /></p>
</div>
<div id="lambda-100-2" class="section level3">
<h3><span class="math inline">\(\lambda = 100\)</span></h3>
<pre class="r"><code>CorNullPlot("friendly", L, lambda = 100, rho)</code></pre>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.0143258263202469 ; 2 : -0.0536731314173197 ; 3 : 0.038023953951068 ; 4 : -0.00847336183440839 ; 5 : 0.0110188598000896 ; 6 : 7.45288780367749e-10 ; 7 : 0.00286984116034979 ; 8 : -2.13984115657199e-11 ; 9 : 0.000166121359692821 ; 10 : 3.84358623366705e-14 ;
Normalized w:
0 : 1 ; 1 : -0.0143258263202469 ; 2 : -0.075905270385407 ; 3 : 0.093139285183201 ; 4 : -0.0415108258005476 ; 5 : 0.120705561409919 ; 6 : 1.99981965092424e-08 ; 7 : 0.20373851123343 ; 8 : -4.29676694120694e-09 ; 9 : 0.1000707128701 ; 10 : 7.32180478817837e-11 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-17-1.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.0393072898699236 ; 2 : -0.106024568009562 ; 3 : -0.097676191395372 ; 4 : -1.16203194074142e-07 ; 5 : -0.0533458972631849 ; 6 : 1.48537530479948e-10 ; 7 : -0.00990567552805969 ; 8 : -1.3037998426785e-11 ; 9 : -0.000640783026514746 ; 10 : -1.80297946645294e-13 ;
Normalized w:
0 : 1 ; 1 : -0.0393072898699236 ; 2 : -0.14994138202387 ; 3 : -0.23925682893709 ; 4 : -5.69277063926509e-07 ; 5 : -0.58437502562799 ; 6 : 3.98568018435733e-09 ; 7 : -0.703233200753983 ; 8 : -2.61800930632923e-09 ; 9 : -0.386004631655817 ; 10 : -3.43456940677709e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-17-2.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.0471983746972584 ; 2 : -0.124083434436633 ; 3 : -0.108707831296981 ; 4 : -6.08969419030976e-08 ; 5 : -0.0429310811444038 ; 6 : -3.60110788740957e-12 ; 7 : -0.00875809871058111 ; 8 : -2.30395448024539e-12 ; 9 : -0.000396989324508739 ; 10 : -1.47000281868042e-13 ;
Normalized w:
0 : 1 ; 1 : -0.0471983746972584 ; 2 : -0.175480475846119 ; 3 : -0.266278717722159 ; 4 : -2.98332869117001e-07 ; 5 : -0.470286431217493 ; 6 : -9.66278643667014e-11 ; 7 : -0.621763328640716 ; 8 : -4.62630387978099e-10 ; 9 : -0.239144471119603 ; 10 : -2.80026855705051e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-17-3.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.0539582788568558 ; 2 : -0.188930502346326 ; 3 : -0.0280893431400025 ; 4 : 0.0228113553937437 ; 5 : -0.00143603651187446 ; 6 : -2.15992130583009e-10 ; 7 : -0.000835287082532969 ; 8 : 2.55982035462218e-13 ; 9 : -6.74604681276957e-06 ; 10 : -1.23321182867123e-13 ;
Normalized w:
0 : 1 ; 1 : 0.0539582788568558 ; 2 : -0.267188078764136 ; 3 : -0.0688045579029532 ; 4 : 0.111752362111914 ; 5 : -0.0157309918190936 ; 6 : -5.79567703906345e-09 ; 7 : -0.0592995002646907 ; 8 : 5.14007847796959e-11 ; 9 : -0.00406378634786777 ; 10 : -2.34919570501963e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-17-4.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.0198056824607031 ; 2 : -4.36733024185824e-08 ; 3 : 0.0118046817897605 ; 4 : -0.0159309096998483 ; 5 : 0.0106919811267829 ; 6 : 2.79418474996273e-11 ; 7 : 0.00145209391072763 ; 8 : -8.53750690386395e-13 ; 9 : 8.26999067968149e-05 ; 10 : 1.07096655108757e-14 ;
Normalized w:
0 : 1 ; 1 : -0.0198056824607031 ; 2 : -6.1763376593981e-08 ; 3 : 0.0289154469608378 ; 4 : -0.0780451998059671 ; 5 : 0.11712478495117 ; 6 : 7.49758445113191e-10 ; 7 : 0.103088441141013 ; 8 : -1.7143177806532e-10 ; 9 : 0.0498180284747919 ; 10 : 2.04012803278531e-11 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-17-5.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.0235595599950422 ; 2 : -0.0729352264288025 ; 3 : -0.00628596902629248 ; 4 : 3.04157194967634e-08 ; 5 : 0.00713729140052068 ; 6 : -9.14136055260368e-10 ; 7 : 0.000591096532765901 ; 8 : -8.65337464892552e-12 ; 9 : 0.000113159486957897 ; 10 : -2.51620231842176e-13 ;
Normalized w:
0 : 1 ; 1 : -0.0235595599950422 ; 2 : -0.103145986390365 ; 3 : -0.0153974166533562 ; 4 : 1.49005985853384e-07 ; 5 : 0.0781851099910563 ; 6 : -2.45288443229482e-08 ; 7 : 0.0419636909682795 ; 8 : -1.73758383921104e-09 ; 9 : 0.0681667339397591 ; 10 : -4.79321681966505e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-17-6.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.00601948530079037 ; 2 : -0.0391864584023975 ; 3 : -0.0145052145385332 ; 4 : -0.000819116183986385 ; 5 : 0.00523031517453755 ; 6 : 6.28472560300545e-09 ; 7 : 0.000921365819989283 ; 8 : -4.73469179333874e-11 ; 9 : 0.000109667614931986 ; 10 : -7.94626799060662e-13 ;
Normalized w:
0 : 1 ; 1 : -0.00601948530079037 ; 2 : -0.0554180209340396 ; 3 : -0.0355303742290065 ; 4 : -0.00401283338164469 ; 5 : 0.0572952320791157 ; 6 : 1.68636884019043e-07 ; 7 : 0.0654104844057311 ; 8 : -9.5071856674691e-09 ; 9 : 0.0660632469256254 ; 10 : -1.5137171247037e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-17-7.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.0213402106789018 ; 2 : -0.0761744254681988 ; 3 : 0.0121255607384809 ; 4 : 1.55458418155982e-08 ; 5 : -0.00177602006117852 ; 6 : -1.42757830930138e-10 ; 7 : -0.000122700667812524 ; 8 : -1.5321263092994e-11 ; 9 : -1.12211778175473e-05 ; 10 : 3.91795484859355e-13 ;
Normalized w:
0 : 1 ; 1 : -0.0213402106789018 ; 2 : -0.107726905603105 ; 3 : 0.0297014366544035 ; 4 : 7.61587601404752e-08 ; 5 : -0.0194553250017836 ; 6 : -3.83059457136253e-09 ; 7 : -0.00871088328262191 ; 8 : -3.07648521262078e-09 ; 9 : -0.00675958387001233 ; 10 : 7.46347260769794e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-17-8.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.012072716551565 ; 2 : -0.104897706018627 ; 3 : -0.0016482914884409 ; 4 : 0.00478541280484129 ; 5 : -0.00410098052086091 ; 6 : -5.26902901614132e-11 ; 7 : -0.000661347566875882 ; 8 : -6.73707428243486e-11 ; 9 : -8.99845589277491e-05 ; 10 : 8.36113326500383e-13 ;
Normalized w:
0 : 1 ; 1 : 0.012072716551565 ; 2 : -0.148347758513368 ; 3 : -0.0040374730940528 ; 4 : 0.023443639160884 ; 5 : -0.0449239907832961 ; 6 : -1.4138288466613e-09 ; 7 : -0.0469510196399583 ; 8 : -1.35279377949696e-08 ; 9 : -0.0542062680913063 ; 10 : 1.59274650944661e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-17-9.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.0584372637118367 ; 2 : -0.159766679353171 ; 3 : -0.16731250025789 ; 4 : 1.39220148390215e-09 ; 5 : -0.0779966027443049 ; 6 : -1.93398400430519e-11 ; 7 : -0.0139452220243767 ; 8 : -4.19305968701226e-14 ; 9 : -0.000704665629971957 ; 10 : 1.44173986190974e-14 ;
Normalized w:
0 : 1 ; 1 : -0.0584372637118367 ; 2 : -0.225944204756567 ; 3 : -0.40983025322111 ; 4 : 6.82036650941168e-09 ; 5 : -0.854409974636502 ; 6 : -5.18942364122839e-10 ; 7 : -0.990012553071007 ; 8 : -8.41959702958714e-12 ; 9 : -0.424487206562392 ; 10 : 2.74642929350048e-11 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-17-10.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.0221386594068507 ; 2 : -0.126212034230156 ; 3 : 0.147703321949132 ; 4 : -4.64299381569152e-08 ; 5 : 0.0667310601145318 ; 6 : -8.09802179093666e-11 ; 7 : 0.0122849862328433 ; 8 : -1.86170370637593e-11 ; 9 : 0.000680553494538148 ; 10 : -1.63034348561158e-12 ;
Normalized w:
0 : 1 ; 1 : 0.0221386594068507 ; 2 : -0.178490770542984 ; 3 : 0.361797772089401 ; 4 : -2.27459314546842e-07 ; 5 : 0.731002138219247 ; 6 : -2.17292726493707e-09 ; 7 : 0.872147504253376 ; 8 : -3.73827137370018e-09 ; 9 : 0.409962171454664 ; 10 : -3.10570805847057e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-17-11.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.0266335902894288 ; 2 : -0.206100134415379 ; 3 : -0.0345510138726153 ; 4 : 0.0208532427113095 ; 5 : -0.0236810318748696 ; 6 : -0.00133824194458075 ; 7 : -0.00375805926144087 ; 8 : -1.11422860372917e-12 ; 9 : -0.000261551522963531 ; 10 : -4.54941002885209e-13 ;
Normalized w:
0 : 1 ; 1 : -0.0266335902894288 ; 2 : -0.291469605297147 ; 3 : -0.0846323540837305 ; 4 : 0.102159608250242 ; 5 : -0.259412706857298 ; 6 : -0.0359087995010887 ; 7 : -0.266795741043607 ; 8 : -2.23735327958657e-10 ; 9 : -0.157557386982741 ; 10 : -8.66635743485219e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-17-12.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.0178736752577191 ; 2 : -3.33297894882455e-09 ; 3 : -0.00880754674749978 ; 4 : -0.00231436528917833 ; 5 : 0.00587465749135139 ; 6 : 1.77477113835265e-11 ; 7 : 0.00117617949938169 ; 8 : 5.66228379357175e-13 ; 9 : 0.000182044741821306 ; 10 : -3.47304260795654e-14 ;
Normalized w:
0 : 1 ; 1 : 0.0178736752577191 ; 2 : -4.7135440325317e-09 ; 3 : -0.021573995417084 ; 4 : -0.0113380280737915 ; 5 : 0.0643536485125974 ; 6 : 4.76221069183346e-10 ; 7 : 0.0835004610910593 ; 8 : 1.13697756215357e-10 ; 9 : 0.109662882136274 ; 10 : -6.61594106403663e-11 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-17-13.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.0100670198787314 ; 2 : -0.0594193512782408 ; 3 : 0.0709943910956656 ; 4 : -0.00557919096143803 ; 5 : 0.0528734045042586 ; 6 : 1.0187436081768e-11 ; 7 : 0.00862078224168945 ; 8 : -3.25336915145547e-13 ; 9 : 0.000594887873495194 ; 10 : 2.78058579403743e-15 ;
Normalized w:
0 : 1 ; 1 : 0.0100670198787314 ; 2 : -0.0840316524450992 ; 3 : 0.17390003278397 ; 4 : -0.0273323420661422 ; 5 : 0.579199126781554 ; 6 : 2.73357595143208e-10 ; 7 : 0.612014826414758 ; 8 : -6.53271340939651e-11 ; 9 : 0.358357610896768 ; 10 : 5.29685172727352e-12 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-17-14.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.755145536903475 ; 2 : -0.129582507148287 ; 3 : 1.57226278196186 ; 4 : -0.00209137058101707 ; 5 : 0.702090740033755 ; 6 : -4.93753339754975e-11 ; 7 : 0.105647798050886 ; 8 : -6.54990111273523e-12 ; 9 : 0.0047908673591942 ; 10 : -6.94806849648922e-13 ;
Normalized w:
0 : 1 ; 1 : 0.755145536903475 ; 2 : -0.183257339055417 ; 3 : 3.85124155737532 ; 4 : -0.0102455815731196 ; 5 : 7.69101871463966 ; 6 : -1.32487923817161e-09 ; 7 : 7.50024962613405 ; 8 : -1.31520970530639e-09 ; 9 : 2.88599559254255 ; 10 : -1.32356601604461e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-17-15.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.0665160046524072 ; 2 : -0.175168821097131 ; 3 : 0.0728023434800905 ; 4 : 0.0124016851804963 ; 5 : 0.0575773053199646 ; 6 : -2.94031619393901e-10 ; 7 : 0.00980624380949297 ; 8 : -3.50977049744981e-12 ; 9 : 0.000729953319692173 ; 10 : 5.7734017138962e-15 ;
Normalized w:
0 : 1 ; 1 : 0.0665160046524072 ; 2 : -0.247726122500469 ; 3 : 0.178328593605059 ; 4 : 0.0607556012857036 ; 5 : 0.630727778482136 ; 6 : -7.88969626198929e-09 ; 7 : 0.696174248993846 ; 8 : -7.04756322605971e-10 ; 9 : 0.439720389952048 ; 10 : 1.09979893107673e-11 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-17-16.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.00942958186553758 ; 2 : -0.132501486906584 ; 3 : -0.0108467867194774 ; 4 : 0.00772879978537314 ; 5 : -8.97741269895399e-05 ; 6 : -1.55430447297507e-10 ; 7 : -0.000342598154157444 ; 8 : -1.53879911171855e-10 ; 9 : -3.1048509866871e-05 ; 10 : 2.7699282816659e-12 ;
Normalized w:
0 : 1 ; 1 : 0.00942958186553758 ; 2 : -0.187385399817893 ; 3 : -0.0265690928115166 ; 4 : 0.0378632315965926 ; 5 : -0.000983426288650087 ; 6 : -4.1706365511651e-09 ; 7 : -0.0243220561624572 ; 8 : -3.08988409353853e-08 ; 9 : -0.018703473904123 ; 10 : 5.27654979559615e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-17-17.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.0032146401682356 ; 2 : -0.134244654152846 ; 3 : -0.00784455575406555 ; 4 : 0.00571811237588096 ; 5 : 0.000394357992006668 ; 6 : -1.97183075993725e-10 ; 7 : -0.000394845955582022 ; 8 : 2.87313262419052e-13 ; 9 : -3.8687191410436e-05 ; 10 : -5.46254762403491e-14 ;
Normalized w:
0 : 1 ; 1 : -0.0032146401682356 ; 2 : -0.189850610579041 ; 3 : -0.0192151588562743 ; 4 : 0.0280129152256039 ; 5 : 0.00431997535908988 ; 6 : -5.2909771432137e-09 ; 7 : -0.0280312821030894 ; 8 : 5.76920452221879e-11 ; 9 : -0.0233049791462286 ; 10 : -1.04058306273911e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-17-18.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.0468977220545989 ; 2 : -0.176515694967991 ; 3 : 0.0086371603609139 ; 4 : 0.0214837985710809 ; 5 : 0.00421092325703564 ; 6 : -3.60972344649366e-09 ; 7 : 0.00118923411980044 ; 8 : 1.56066251015029e-11 ; 9 : 0.000117942469740798 ; 10 : -4.27039448710873e-13 ;
Normalized w:
0 : 1 ; 1 : -0.0468977220545989 ; 2 : -0.249630889795445 ; 3 : 0.021156635710832 ; 4 : 0.105248688471765 ; 5 : 0.0461283531160309 ; 6 : -9.68590440760158e-08 ; 7 : 0.084427247202284 ; 8 : 3.13378544916739e-09 ; 9 : 0.0710479799012381 ; 10 : -8.13484930538227e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-17-19.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.00251787185842929 ; 2 : -0.168618656858548 ; 3 : 0.03223575211743 ; 4 : 0.0179165970080232 ; 5 : 0.0123936722249901 ; 6 : -1.68320195603717e-11 ; 7 : 0.00246049593551517 ; 8 : 8.37815192347735e-14 ; 9 : 0.000147420124064493 ; 10 : -6.70767119436693e-15 ;
Normalized w:
0 : 1 ; 1 : -0.00251787185842929 ; 2 : -0.238462791398494 ; 3 : 0.078961144162546 ; 4 : 0.0877730411934653 ; 5 : 0.135765876959047 ; 6 : -4.51650479227166e-10 ; 7 : 0.174677883126001 ; 8 : 1.68231955454474e-11 ; 9 : 0.0888051779362482 ; 10 : -1.27777174968143e-11 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-17-20.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.0191148249070555 ; 2 : -0.136481631225831 ; 3 : 0.00291643180343143 ; 4 : 0.0123743506241611 ; 5 : 0.000209611834436676 ; 6 : -1.01131666064357e-09 ; 7 : 0.000344121189713614 ; 8 : -6.05400685949404e-13 ; 9 : 2.84537029045289e-05 ; 10 : -3.62249356682074e-13 ;
Normalized w:
0 : 1 ; 1 : 0.0191148249070555 ; 2 : -0.193014173894374 ; 3 : 0.00714376978803194 ; 4 : 0.0606216898549702 ; 5 : 0.00229618260082011 ; 6 : -2.71364735997254e-08 ; 7 : 0.0244301809608108 ; 8 : -1.21563492952842e-10 ; 9 : 0.017140374595509 ; 10 : -6.9006363146921e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-17-21.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.0643220952335851 ; 2 : -0.0495756418883013 ; 3 : -0.104658478278025 ; 4 : -0.000897793483634867 ; 5 : -0.06719758684831 ; 6 : 8.1660347993526e-12 ; 7 : -0.0108335701580218 ; 8 : -6.15090891031505e-13 ; 9 : -0.000610394136711532 ; 10 : -3.84944645309717e-14 ;
Normalized w:
0 : 1 ; 1 : -0.0643220952335851 ; 2 : -0.0701105451217874 ; 3 : -0.256359869037317 ; 4 : -0.00439827185860237 ; 5 : -0.736112682534638 ; 6 : 2.19117707015775e-10 ; 7 : -0.769107184687973 ; 8 : -1.23509270690709e-10 ; 9 : -0.367698509724466 ; 10 : -7.33296816011143e-11 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-17-22.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.0589721054760297 ; 2 : -0.0897555934468185 ; 3 : -0.0313298482559382 ; 4 : 1.10541952772606e-07 ; 5 : -0.00229180342357664 ; 6 : -9.74836814540392e-10 ; 7 : -0.00125037947131985 ; 8 : 9.60506762493466e-12 ; 9 : -6.5803675390294e-05 ; 10 : -4.62945221399911e-14 ;
Normalized w:
0 : 1 ; 1 : 0.0589721054760297 ; 2 : -0.126933577551336 ; 3 : -0.0767421419458741 ; 4 : 5.41542758927443e-07 ; 5 : -0.0251054486492099 ; 6 : -2.61576166113801e-08 ; 7 : -0.088768136537738 ; 8 : 1.92868227214546e-09 ; 9 : -0.0396398194546198 ; 10 : -8.81883307058329e-11 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-17-23.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.0776287643820075 ; 2 : -0.0832306955092176 ; 3 : 0.00600127913755874 ; 4 : 2.47278681546533e-08 ; 5 : -0.00938702983166618 ; 6 : -9.24665827443709e-11 ; 7 : -0.00147181641348643 ; 8 : -4.79113522282634e-11 ; 9 : -0.000111377475592741 ; 10 : 1.2383289318526e-12 ;
Normalized w:
0 : 1 ; 1 : -0.0776287643820075 ; 2 : -0.117705978394881 ; 3 : 0.0147000716910288 ; 4 : 1.21141318811436e-07 ; 5 : -0.10282975973555 ; 6 : -2.48113877596227e-09 ; 7 : -0.104488599939135 ; 8 : -9.62052317437975e-09 ; 9 : -0.0670932588129991 ; 10 : 2.35894348438433e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-17-24.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.0753958788269554 ; 2 : -0.00407553005654872 ; 3 : -0.0113385924414496 ; 4 : -0.0132336109957749 ; 5 : -0.0156953345608941 ; 6 : 2.33497774479345e-11 ; 7 : -0.00209047158649764 ; 8 : -5.04696944617978e-13 ; 9 : -0.000181781026995448 ; 10 : 6.38545877212385e-15 ;
Normalized w:
0 : 1 ; 1 : 0.0753958788269554 ; 2 : -0.00576366987983038 ; 3 : -0.0277737658829298 ; 4 : -0.0648311887882667 ; 5 : -0.171933775731842 ; 6 : 6.26540275596879e-10 ; 7 : -0.148408760280274 ; 8 : -1.01342342178179e-10 ; 9 : -0.10950402158597 ; 10 : 1.21639218610288e-11 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-17-25.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.0122895833972033 ; 2 : -0.0244580158176761 ; 3 : 0.0674670143136826 ; 4 : -0.00752437004938331 ; 5 : 0.0401583101667782 ; 6 : 1.03320569137854e-11 ; 7 : 0.00805046894626414 ; 8 : -1.97027692060111e-13 ; 9 : 0.000479828726098487 ; 10 : 4.52651873003537e-15 ;
Normalized w:
0 : 1 ; 1 : 0.0122895833972033 ; 2 : -0.0345888576780932 ; 3 : 0.165259759537571 ; 4 : -0.0368617345137387 ; 5 : 0.439912246992669 ; 6 : 2.77238179279449e-10 ; 7 : 0.571526598929575 ; 8 : -3.95628465760705e-11 ; 9 : 0.289046530590748 ; 10 : 8.62275086247565e-12 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-17-26.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.0240187003585077 ; 2 : -0.113626133688216 ; 3 : 0.000156192994302674 ; 4 : 0.00396861511292672 ; 5 : -0.000220000356935625 ; 6 : -1.26192135831622e-11 ; 7 : 0.000132645205657432 ; 8 : -6.8435261571628e-11 ; 9 : -1.49657441041091e-05 ; 10 : 8.64410998450281e-13 ;
Normalized w:
0 : 1 ; 1 : 0.0240187003585077 ; 2 : -0.160691619301894 ; 3 : 0.000382593137438991 ; 4 : 0.0194421640243366 ; 5 : -0.0024099831630566 ; 6 : -3.38609032734473e-10 ; 7 : 0.0094168754341803 ; 8 : -1.37416914629723e-08 ; 9 : -0.00901529269865721 ; 10 : 1.64665190336291e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-17-27.png" width="672" style="display: block; margin: auto;" /></p>
</div>
</div>
<div id="iid" class="section level2">
<h2>IID</h2>
<div id="no-regularization-lambda-0-3" class="section level3">
<h3>No regularization: <span class="math inline">\(\lambda = 0\)</span></h3>
<pre class="r"><code>CorNullPlot("iid", L, lambda = 0, rho)</code></pre>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 0.9902233
Unnormalized w:
0 : 1 ; 1 : -0.0405368510281718 ; 2 : -0.200589095951288 ; 3 : -0.120752088126515 ; 4 : -0.362460941188633 ; 5 : -0.0832233990756255 ; 6 : -0.165826806753714 ; 7 : -0.0178231676620004 ; 8 : -0.0259697707667603 ; 9 : -0.00113612103796531 ; 10 : -0.00129362995115145 ;
Normalized w:
0 : 1 ; 1 : -0.0405368510281718 ; 2 : -0.283675819958469 ; 3 : -0.29578100128555 ; 4 : -1.77568871520219 ; 5 : -0.911666659719494 ; 6 : -4.44960014871631 ; 7 : -1.26531938251147 ; 8 : -5.21468858371236 ; 9 : -0.684393881594384 ; 10 : -2.46428866028979 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-18-1.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.0230825311326855 ; 2 : -0.425056423146347 ; 3 : -0.113624582563346 ; 4 : -0.724398854107389 ; 5 : -0.0757983243687847 ; 6 : -0.317560886039965 ; 7 : -0.0153874489963285 ; 8 : -0.0481496570455215 ; 9 : -0.000992705709733054 ; 10 : -0.00231290478163741 ;
Normalized w:
0 : 1 ; 1 : -0.0230825311326855 ; 2 : -0.601120558387361 ; 3 : -0.278322249516936 ; 4 : -3.54881512563988 ; 5 : -0.830329041557538 ; 6 : -8.52105273816511 ; 7 : -1.09240051104786 ; 8 : -9.66837440191504 ; 9 : -0.598001173520966 ; 10 : -4.40594701803701 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-18-2.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.613516326876289 ; 2 : -1.71966778986634 ; 3 : -2.04701724129729 ; 4 : -2.69287715555184 ; 5 : -1.28761408547499 ; 6 : -1.07449246583325 ; 7 : -0.246065256474665 ; 8 : -0.146087556394099 ; 9 : -0.0137289731568745 ; 10 : -0.00617882053884931 ;
Normalized w:
0 : 1 ; 1 : -0.613516326876289 ; 2 : -2.43197751120514 ; 3 : -5.01414773585802 ; 4 : -13.1923499421988 ; 5 : -14.1051055995207 ; 6 : -28.8316583389743 ; 7 : -17.4689002698359 ; 8 : -29.3341485141565 ; 9 : -8.2702677929157 ; 10 : -11.7702882298752 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-18-3.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 0.9980103
Unnormalized w:
0 : 1 ; 1 : -0.000902347084345419 ; 2 : -0.00929193336098981 ; 3 : 0.00122931259673249 ; 4 : -0.00142235077580944 ; 5 : 0.000175604808176825 ; 6 : -0.000642308271362263 ; 7 : -0.000466993246917224 ; 8 : -0.000443297294507876 ; 9 : -9.44602351401145e-05 ; 10 : -4.03200251011892e-05 ;
Normalized w:
0 : 1 ; 1 : -0.000902347084345419 ; 2 : -0.0131407781797788 ; 3 : 0.00301118859637039 ; 4 : -0.00696806727196982 ; 5 : 0.00192365429289629 ; 6 : -0.0172349394873168 ; 7 : -0.0331532316831724 ; 8 : -0.0890133902845065 ; 9 : -0.0569023940438951 ; 10 : -0.0768072666770125 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-18-4.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 0.9984696
Unnormalized w:
0 : 1 ; 1 : -0.0678345291419158 ; 2 : -0.127875725147021 ; 3 : -0.19815560637456 ; 4 : -0.192919650010789 ; 5 : -0.135583981859309 ; 6 : -0.0812520812583151 ; 7 : -0.0291786189131145 ; 8 : -0.011657730511468 ; 9 : -0.00193796793321842 ; 10 : -0.000534479727395144 ;
Normalized w:
0 : 1 ; 1 : -0.0678345291419158 ; 2 : -0.180843584801212 ; 3 : -0.485380125289465 ; 4 : -0.945109407765496 ; 5 : -1.48524810601429 ; 6 : -2.18022212408315 ; 7 : -2.07147644940774 ; 8 : -2.34085370857247 ; 9 : -1.16742261774867 ; 10 : -1.01815231643507 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-18-5.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.0114727533854214 ; 2 : -0.0498172438639265 ; 3 : 0.0118116253548837 ; 4 : -0.0876621303977918 ; 5 : 0.0122992521414138 ; 6 : -0.0418953150673728 ; 7 : 0.00296493266200861 ; 8 : -0.00727741873704751 ; 9 : 0.000167956994609338 ; 10 : -0.000404990350610407 ;
Normalized w:
0 : 1 ; 1 : 0.0114727533854214 ; 2 : -0.0704522219124128 ; 3 : 0.0289324551523852 ; 4 : -0.429454978479825 ; 5 : 0.134731556765921 ; 6 : -1.124169269153 ; 7 : 0.21048933815953 ; 8 : -1.46129408487306 ; 9 : 0.101176490567831 ; 10 : -0.771482700789114 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-18-6.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.0111350267594512 ; 2 : -0.0266795754280783 ; 3 : 0.00735902687801976 ; 4 : -0.04969029447569 ; 5 : 0.00444416788353204 ; 6 : -0.0257308218227747 ; 7 : 0.00117443324760944 ; 8 : -0.0045212416856049 ; 9 : 9.27190608304607e-05 ; 10 : -0.000277156676507209 ;
Normalized w:
0 : 1 ; 1 : 0.0111350267594512 ; 2 : -0.0377306174087443 ; 3 : 0.0180258608545751 ; 4 : -0.243431733268157 ; 5 : 0.0486834199830098 ; 6 : -0.690430400551911 ; 7 : 0.0833764895133866 ; 8 : -0.907858125274839 ; 9 : 0.055853518964132 ; 10 : -0.527967100972262 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-18-7.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 1
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 0.9978326
Unnormalized w:
0 : 1 ; 1 : 0.0180544709284733 ; 2 : -0.00245783703720842 ; 3 : -0.00904400112602128 ; 4 : -0.0121003298721484 ; 5 : -0.00431352381836661 ; 6 : -0.00603469856203478 ; 7 : -0.00120174108668015 ; 8 : -0.00101078435328561 ; 9 : -0.000126542717233364 ; 10 : -7.9486861087073e-05 ;
Normalized w:
0 : 1 ; 1 : 0.0180544709284733 ; 2 : -0.00347590647212305 ; 3 : -0.0221531879919086 ; 4 : -0.0592792678122407 ; 5 : -0.0472522859531041 ; 6 : -0.16192795450116 ; 7 : -0.0853151537691429 ; 8 : -0.202963887321641 ; 9 : -0.0762287278738752 ; 10 : -0.151417776192143 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-18-8.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.014510857364203 ; 2 : -0.0378709798938841 ; 3 : -0.028495844643426 ; 4 : -0.0809425395645655 ; 5 : -0.0173478237591951 ; 6 : -0.0371667594137445 ; 7 : -0.00362382754798107 ; 8 : -0.00631923635224205 ; 9 : -0.000257740809238301 ; 10 : -0.00037179177859789 ;
Normalized w:
0 : 1 ; 1 : -0.014510857364203 ; 2 : -0.0535576533862897 ; 3 : -0.0698002791660149 ; 4 : -0.396535840836449 ; 5 : -0.190035887930704 ; 6 : -0.997288806630154 ; 7 : -0.257266234728603 ; 8 : -1.26889258899406 ; 9 : -0.155261831253286 ; 10 : -0.70824138168125 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-18-9.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.008320705374618 ; 2 : -0.0081291496366805 ; 3 : -0.0096852017391271 ; 4 : -0.0138113022001979 ; 5 : -0.00332037463451784 ; 6 : -0.00558679643695842 ; 7 : -0.00152085258308833 ; 8 : -0.00102829757487779 ; 9 : -8.98800426631903e-05 ; 10 : -5.748078464503e-05 ;
Normalized w:
0 : 1 ; 1 : -0.008320705374618 ; 2 : -0.0114963536667539 ; 3 : -0.0237238023167776 ; 4 : -0.067661286147727 ; 5 : -0.0363728817338679 ; 6 : -0.149909479313912 ; 7 : -0.107969822638604 ; 8 : -0.206480514307723 ; 9 : -0.0541433079932174 ; 10 : -0.109497500161639 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-18-10.png" width="672" style="display: block; margin: auto;" /></p>
</div>
<div id="lambda-1-3" class="section level3">
<h3><span class="math inline">\(\lambda = 1\)</span></h3>
<pre class="r"><code>CorNullPlot("iid", L, lambda = 1, rho)</code></pre>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 0.9902233
Unnormalized w:
0 : 1 ; 1 : -0.0197501799658939 ; 2 : -0.0480028667210606 ; 3 : -0.0379275988314252 ; 4 : -0.0762234482638905 ; 5 : -0.0261218473505986 ; 6 : -0.033995638241429 ; 7 : -0.00603267327179404 ; 8 : -0.00516302161997914 ; 9 : -0.000418538277949043 ; 10 : -0.00024393677511157 ;
Normalized w:
0 : 1 ; 1 : -0.0197501799658939 ; 2 : -0.067886305149712 ; 3 : -0.0929032643059713 ; 4 : -0.373417109363928 ; 5 : -0.286150500752588 ; 6 : -0.91219869655592 ; 7 : -0.428277316575674 ; 8 : -1.03672651333626 ; 9 : -0.252125457648748 ; 10 : -0.464685150649179 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-19-1.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.00218244400583294 ; 2 : -0.0950816757643174 ; 3 : -0.0336218589432436 ; 4 : -0.135504581690652 ; 5 : -0.0236811368702788 ; 6 : -0.0565322409458715 ; 7 : -0.00504139993758648 ; 8 : -0.00857394331796279 ; 9 : -0.000382388078553011 ; 10 : -0.000416126261459722 ;
Normalized w:
0 : 1 ; 1 : -0.00218244400583294 ; 2 : -0.134465795399059 ; 3 : -0.0823563986147782 ; 4 : -0.663834165902754 ; 5 : -0.259413857024379 ; 6 : -1.51691920410439 ; 7 : -0.3579038909913 ; 8 : -1.72163415453802 ; 9 : -0.230348750362903 ; 10 : -0.792695953314336 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-19-2.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.170195270010404 ; 2 : -0.486597915290635 ; 3 : -0.551898117003095 ; 4 : -0.676471730529319 ; 5 : -0.35279778951818 ; 6 : -0.260883986493315 ; 7 : -0.070447875520796 ; 8 : -0.0349150352172874 ; 9 : -0.00416576004253135 ; 10 : -0.00146605118681346 ;
Normalized w:
0 : 1 ; 1 : -0.170195270010404 ; 2 : -0.688153371226491 ; 3 : -1.35186877666043 ; 4 : -3.3140211304287 ; 5 : -3.86470615114134 ; 6 : -7.00025193648227 ; 7 : -5.0013030255708 ; 8 : -7.01088342992012 ; 9 : -2.50943393355759 ; 10 : -2.79274093171165 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-19-3.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 0.9980103
Unnormalized w:
0 : 1 ; 1 : -0.00128479518161606 ; 2 : -0.00832171681123837 ; 3 : 0.00140763563409998 ; 4 : 0.00161652795446755 ; 5 : 0.000646152140337805 ; 6 : 0.0013397558971381 ; 7 : -0.000308649891301932 ; 8 : -8.66346212930184e-08 ; 9 : -7.81111060511662e-05 ; 10 : -4.36195964604597e-06 ;
Normalized w:
0 : 1 ; 1 : -0.00128479518161606 ; 2 : -0.0117686847766815 ; 3 : 0.00344798904730399 ; 4 : 0.00791933728678106 ; 5 : 0.00707824205686519 ; 6 : 0.0359494231110842 ; 7 : -0.0219119685838471 ; 8 : -1.73960938919487e-05 ; 9 : -0.0470537568441898 ; 10 : -0.00830927552568261 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-19-4.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 0.9984696
Unnormalized w:
0 : 1 ; 1 : -0.0325775610993165 ; 2 : -0.0543974101114557 ; 3 : -0.0720847214087252 ; 4 : -0.0659493507450574 ; 5 : -0.0488700460508899 ; 6 : -0.0266000567192026 ; 7 : -0.0106871935286174 ; 8 : -0.00356002770595598 ; 9 : -0.000735016804039403 ; 10 : -0.000147615066641242 ;
Normalized w:
0 : 1 ; 1 : -0.0325775610993165 ; 2 : -0.0769295551375921 ; 3 : -0.176570785702055 ; 4 : -0.323084516386456 ; 5 : -0.535344532167773 ; 6 : -0.713754420353845 ; 7 : -0.758715474872715 ; 8 : -0.714847889982522 ; 9 : -0.442770608714831 ; 10 : -0.281197984391246 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-19-5.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.00673381506404109 ; 2 : -0.0138407751387194 ; 3 : -0.00392500107492052 ; 4 : -0.0137266308999818 ; 5 : -0.000357400315025183 ; 6 : -0.0054372337726941 ; 7 : -0.000124146427110371 ; 8 : -0.000995463543661852 ; 9 : -5.37901252722243e-05 ; 10 : -4.40677105680697e-05 ;
Normalized w:
0 : 1 ; 1 : 0.00673381506404109 ; 2 : -0.0195738119149333 ; 3 : -0.00961424987343076 ; 4 : -0.067246483184952 ; 5 : -0.00391512429197491 ; 6 : -0.14589629190362 ; 7 : -0.0088135220108606 ; 8 : -0.199887493164919 ; 9 : -0.0324029142990219 ; 10 : -0.0839463861679815 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-19-6.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.0111556935543884 ; 2 : -0.00308411410458595 ; 3 : 0.00432919802742235 ; 4 : -0.00431515761454924 ; 5 : 0.00192971775723357 ; 6 : -0.00277604341683021 ; 7 : 0.000651520347601133 ; 8 : -0.000371668518460222 ; 9 : 6.40150039107466e-05 ; 10 : -2.33385566220332e-05 ;
Normalized w:
0 : 1 ; 1 : 0.0111556935543884 ; 2 : -0.00436159599461161 ; 3 : 0.0106043261626482 ; 4 : -0.0211398686306622 ; 5 : 0.0211389989051021 ; 6 : -0.0744890614622777 ; 7 : 0.0462533562806532 ; 8 : -0.0746304462040344 ; 9 : 0.0385623323067918 ; 10 : -0.0444585720823917 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-19-7.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 1
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 0.9978326
Unnormalized w:
0 : 1 ; 1 : 0.0191703735008943 ; 2 : 0.00235392083903741 ; 3 : -0.00531344730659793 ; 4 : -0.00223273858618263 ; 5 : -0.00190779557192878 ; 6 : -0.000747781072324904 ; 7 : -0.000733454988207041 ; 8 : 9.39725292070835e-08 ; 9 : -9.8774216023983e-05 ; 10 : -1.00587465533097e-05 ;
Normalized w:
0 : 1 ; 1 : 0.0191703735008943 ; 2 : 0.00332894677531937 ; 3 : -0.0130152346763305 ; 4 : -0.0109381405303411 ; 5 : -0.0208988533970773 ; 6 : -0.0200650717200741 ; 7 : -0.0520701387305429 ; 8 : 1.88695341071694e-05 ; 9 : -0.0595011155036459 ; 10 : -0.0191613181543815 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-19-8.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.00790992082874686 ; 2 : 0.002662954886282 ; 3 : -0.0047311806006799 ; 4 : -0.00691435335304447 ; 5 : -0.00168321396850534 ; 6 : -0.0015471503714363 ; 7 : -0.000315470776571894 ; 8 : -0.000178408590570786 ; 9 : -4.0369240933949e-05 ; 10 : -1.71817234863898e-05 ;
Normalized w:
0 : 1 ; 1 : -0.00790992082874686 ; 2 : 0.00376598691616771 ; 3 : -0.0115889783526202 ; 4 : -0.0338732752325218 ; 5 : -0.0184386851931633 ; 6 : -0.0415144008233474 ; 7 : -0.0223962034012286 ; 8 : -0.0358241606690066 ; 9 : -0.0243182377374899 ; 10 : -0.0327301685571348 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-19-9.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.0074475785728308 ; 2 : -0.00345757783165271 ; 3 : -0.0061470003353478 ; 4 : -0.00440828057441714 ; 5 : -0.000604679039560331 ; 6 : -0.000693235748723768 ; 7 : -0.000867998410912082 ; 8 : -0.000110162462776587 ; 9 : -4.01317704379318e-05 ; 10 : -2.9061910493349e-11 ;
Normalized w:
0 : 1 ; 1 : -0.0074475785728308 ; 2 : -0.00488975346248383 ; 3 : -0.0150570142703192 ; 4 : -0.0215960761006903 ; 5 : -0.00662392700035504 ; 6 : -0.0186014671029517 ; 7 : -0.0616217742067147 ; 8 : -0.0221204469671325 ; 9 : -0.0241751866460108 ; 10 : -5.53612232086703e-08 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-19-10.png" width="672" style="display: block; margin: auto;" /></p>
</div>
<div id="lambda-10-3" class="section level3">
<h3><span class="math inline">\(\lambda = 10\)</span></h3>
<pre class="r"><code>CorNullPlot("iid", L, lambda = 10, rho)</code></pre>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 0.9902233
Unnormalized w:
0 : 1 ; 1 : -0.0137879535328333 ; 2 : 0.00266974779862749 ; 3 : -0.012641051669197 ; 4 : 0.000579032181585961 ; 5 : -0.00750074964225723 ; 6 : -0.000349552094298496 ; 7 : -0.00189888638839369 ; 8 : -1.6651506183022e-10 ; 9 : -0.000142379793050877 ; 10 : -4.50587775942304e-12 ;
Normalized w:
0 : 1 ; 1 : -0.0137879535328333 ; 2 : 0.00377559354493471 ; 3 : -0.0309641264016902 ; 4 : 0.00283666677907235 ; 5 : -0.0821665955452618 ; 6 : -0.00937946693434626 ; 7 : -0.134807560473347 ; 8 : -3.34359590518067e-08 ; 9 : -0.0857689066309411 ; 10 : -8.583431032433e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-20-1.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.00435786450452107 ; 2 : -0.00264411653921755 ; 3 : -0.00827250497601338 ; 4 : -0.00208988507645332 ; 5 : -0.00599799001026069 ; 6 : -0.000115650745348266 ; 7 : -0.0011841001957846 ; 8 : -2.43441845706757e-12 ; 9 : -0.000124791375770825 ; 10 : 7.20910129199417e-14 ;
Normalized w:
0 : 1 ; 1 : 0.00435786450452107 ; 2 : -0.00373934547025647 ; 3 : -0.0202634160858676 ; 4 : -0.0102383041167361 ; 5 : -0.0657046885662085 ; 6 : -0.00310323513896687 ; 7 : -0.0840627747533471 ; 8 : -4.88827346612446e-10 ; 9 : -0.0751737281498222 ; 10 : 1.37329122203215e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-20-2.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.0213906544699513 ; 2 : -0.0064965131610548 ; 3 : -0.0539805647596282 ; 4 : -0.00450372706774079 ; 5 : -0.0306417865494322 ; 6 : -0.00167769276716086 ; 7 : -0.00647651477907918 ; 8 : -4.78139909125402e-11 ; 9 : -0.000386234643916067 ; 10 : -2.22787960891607e-13 ;
Normalized w:
0 : 1 ; 1 : -0.0213906544699513 ; 2 : -0.00918745702049901 ; 3 : -0.132224839688352 ; 4 : -0.0220636665134521 ; 5 : -0.335663953907648 ; 6 : -0.045017220872777 ; 7 : -0.459786937793475 ; 8 : -9.60097317734063e-09 ; 9 : -0.232665902947581 ; 10 : -4.2439790852523e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-20-3.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 0.9980103
Unnormalized w:
0 : 1 ; 1 : -0.00201772460477806 ; 2 : -0.00818676279956309 ; 3 : 0.000119339197742771 ; 4 : 5.07400940916174e-06 ; 5 : 0.000104861491893788 ; 6 : 0.000855148935229326 ; 7 : -0.000369237660837132 ; 8 : -9.6006144765198e-10 ; 9 : -7.66743893857349e-05 ; 10 : -4.6483395267771e-11 ;
Normalized w:
0 : 1 ; 1 : -0.00201772460477806 ; 2 : -0.0115778309830737 ; 3 : 0.000292320140782892 ; 4 : 2.4857468005054e-05 ; 5 : 0.00114870009047746 ; 6 : 0.022946053800712 ; 7 : -0.0262132735252506 ; 8 : -1.92778808704044e-07 ; 9 : -0.0461882855937261 ; 10 : -8.85481228601559e-08 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-20-4.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 0.9984696
Unnormalized w:
0 : 1 ; 1 : -0.0215033313300145 ; 2 : -0.00856616298487061 ; 3 : -0.0293302173171465 ; 4 : -0.00176588048082007 ; 5 : -0.0180265368132136 ; 6 : -0.000937203111658442 ; 7 : -0.00377598139841106 ; 8 : -1.02576741739946e-11 ; 9 : -0.000257194015160242 ; 10 : 2.35019992082386e-12 ;
Normalized w:
0 : 1 ; 1 : -0.0215033313300145 ; 2 : -0.0121143838707024 ; 3 : -0.0718440664719519 ; 4 : -0.00865101224949958 ; 5 : -0.197470816925887 ; 6 : -0.0251477983967112 ; 7 : -0.268068086549999 ; 8 : -2.05972462718213e-09 ; 9 : -0.154932445114829 ; 10 : 4.47699205568421e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-20-5.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.00496843770093787 ; 2 : -0.00433655506640026 ; 3 : -0.00814842666690878 ; 4 : -0.000329110343349857 ; 5 : -0.00347406629700626 ; 6 : 1.16070217052422e-07 ; 7 : -0.000879552022845182 ; 8 : -6.97603471302503e-09 ; 9 : -0.000109013313833644 ; 10 : 2.10299078875745e-11 ;
Normalized w:
0 : 1 ; 1 : 0.00496843770093787 ; 2 : -0.00613281498888101 ; 3 : -0.019959487540414 ; 4 : -0.00161230482055865 ; 5 : -0.0380564895427754 ; 6 : 3.11449074590844e-06 ; 7 : -0.0624419992864651 ; 8 : -1.40077665314452e-06 ; 9 : -0.0656690990721294 ; 10 : 4.00607325828848e-08 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-20-6.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.0109676444502299 ; 2 : -1.44818541486029e-05 ; 3 : 0.0037142436442326 ; 4 : -6.61719149982427e-06 ; 5 : 0.00148940248647299 ; 6 : -0.000265612498956955 ; 7 : 0.000544712261023606 ; 8 : 1.64490757863574e-10 ; 9 : 5.61722206339259e-05 ; 10 : -1.32019803446206e-11 ;
Normalized w:
0 : 1 ; 1 : 0.0109676444502299 ; 2 : -2.04804345452633e-05 ; 3 : 0.00909800170874537 ; 4 : -3.24174854097032e-05 ; 5 : 0.0163155867809108 ; 6 : -0.00712713124009611 ; 7 : 0.0386707343405788 ; 8 : 3.30294820412995e-08 ; 9 : 0.033837877156362 ; 10 : -2.51489928999088e-08 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-20-7.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 1
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 0.9978326
Unnormalized w:
0 : 1 ; 1 : 0.0197279154849016 ; 2 : 0.00131792422353716 ; 3 : -0.00512442464768514 ; 4 : -0.00108226195876817 ; 5 : -0.00195757088089246 ; 6 : -0.000259976149216675 ; 7 : -0.000745269206970503 ; 8 : 7.39184063764335e-09 ; 9 : -9.6954899924885e-05 ; 10 : -9.08393227679978e-11 ;
Normalized w:
0 : 1 ; 1 : 0.0197279154849016 ; 2 : 0.00186382631110628 ; 3 : -0.01255222561217 ; 4 : -0.00530197913401414 ; 5 : -0.0214441145876012 ; 6 : -0.00697589210612538 ; 7 : -0.0529088650598985 ; 8 : 1.48426982016632e-06 ; 9 : -0.0584051681835093 ; 10 : -1.73043545262948e-07 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-20-8.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.00742374059343939 ; 2 : 0.00271226649645315 ; 3 : -0.00332761072202119 ; 4 : -0.00376944630255119 ; 5 : -0.000662021649749187 ; 6 : -6.14923846990956e-05 ; 7 : -3.58501190457403e-05 ; 8 : 1.49206710310614e-11 ; 9 : -1.64480673216069e-05 ; 10 : -4.64340318850247e-13 ;
Normalized w:
0 : 1 ; 1 : -0.00742374059343939 ; 2 : 0.0038357240640542 ; 3 : -0.00815094833156624 ; 4 : -0.0184664401081422 ; 5 : -0.00725208382248828 ; 6 : -0.00165001382742895 ; 7 : -0.00254510597409862 ; 8 : 2.99604696498097e-09 ; 9 : -0.00990823711804553 ; 10 : -8.84540885312298e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-20-9.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.00778028617573776 ; 2 : -0.00211826758992109 ; 3 : -0.00542800064313431 ; 4 : -0.00280486798956937 ; 5 : 0.000365025323946987 ; 6 : -8.79554711790981e-07 ; 7 : -0.000572064645063383 ; 8 : -6.24138534790182e-10 ; 9 : -1.22694277035174e-05 ; 10 : 4.09597720972399e-11 ;
Normalized w:
0 : 1 ; 1 : -0.00778028617573776 ; 2 : -0.00299568275440178 ; 3 : -0.013295831899178 ; 4 : -0.0137409907406221 ; 5 : 0.00399865207972791 ; 6 : -2.36009295059384e-05 ; 7 : -0.0406125609754265 ; 8 : -1.25326023138838e-07 ; 9 : -0.0073910445897476 ; 10 : 7.80259469235692e-08 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-20-10.png" width="672" style="display: block; margin: auto;" /></p>
</div>
<div id="lambda-100-3" class="section level3">
<h3><span class="math inline">\(\lambda = 100\)</span></h3>
<pre class="r"><code>CorNullPlot("iid", L, lambda = 100, rho)</code></pre>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 0.9902233
Unnormalized w:
0 : 1 ; 1 : -0.0134899430951596 ; 2 : 1.25578990189511e-07 ; 3 : -0.0119886801444646 ; 4 : 1.19048130384211e-08 ; 5 : -0.00702900186585543 ; 6 : -7.66463299827262e-10 ; 7 : -0.00177773456643075 ; 8 : -9.22062335550194e-12 ; 9 : -0.000133357895330528 ; 10 : 5.05819082768219e-13 ;
Normalized w:
0 : 1 ; 1 : -0.0134899430951596 ; 2 : 1.77595511075124e-07 ; 3 : -0.0293661490433743 ; 4 : 5.8321434854728e-08 ; 5 : -0.0769988575734984 ; 6 : -2.05663684880707e-08 ; 7 : -0.12620663433814 ; 8 : -1.85148647550599e-09 ; 9 : -0.0803341585769528 ; 10 : 9.63555481004764e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-21-1.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.0042641276489915 ; 2 : -5.27098034943002e-09 ; 3 : -0.0083918204009518 ; 4 : -8.52076344525011e-10 ; 5 : -0.00610190484090151 ; 6 : -1.94653968302033e-11 ; 7 : -0.00121135815458939 ; 8 : -1.08163870997325e-13 ; 9 : -0.000126616634693547 ; 10 : 1.63685754758784e-14 ;
Normalized w:
0 : 1 ; 1 : 0.0042641276489915 ; 2 : -7.45429189716602e-09 ; 3 : -0.0205556779954101 ; 4 : -4.1743045319644e-09 ; 5 : -0.0668430185022345 ; 6 : -5.22311406256123e-10 ; 7 : -0.0859978978615098 ; 8 : -2.1719132922876e-11 ; 9 : -0.0762732553984979 ; 10 : 3.11811696184068e-11 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-21-2.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.0203572279310974 ; 2 : -2.99792271559574e-09 ; 3 : -0.0518605547470987 ; 4 : -8.57609743521251e-11 ; 5 : -0.0291946788546736 ; 6 : -4.19801342447367e-11 ; 7 : -0.00613247110857061 ; 8 : 5.17774964546258e-13 ; 9 : -0.000361745147925575 ; 10 : 5.70725611445673e-15 ;
Normalized w:
0 : 1 ; 1 : -0.0203572279310974 ; 2 : -4.23970296334187e-09 ; 3 : -0.127031896908064 ; 4 : -4.20141254013243e-10 ; 5 : -0.319811683356476 ; 6 : -1.12644520650958e-09 ; 7 : -0.435362260150285 ; 8 : 1.03968387738229e-10 ; 9 : -0.217913547644629 ; 10 : 1.08719858501318e-11 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-21-3.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 0.9980103
Unnormalized w:
0 : 1 ; 1 : -0.00302824675324517 ; 2 : -3.26334368255717e-06 ; 3 : -0.00144537428214117 ; 4 : -1.2565620634739e-08 ; 5 : -0.000735176889291692 ; 6 : 7.28988596753944e-09 ; 7 : -0.000564838893939966 ; 8 : -1.21283093383695e-10 ; 9 : -9.06898368249016e-05 ; 10 : -2.38358555415901e-12 ;
Normalized w:
0 : 1 ; 1 : -0.00302824675324517 ; 2 : -4.61506489455691e-06 ; 3 : -0.00354042947858739 ; 4 : -6.15587177129955e-08 ; 5 : -0.00805345932043076 ; 6 : 1.9560816685968e-07 ; 7 : -0.0400995835337589 ; 8 : -2.43534518708488e-08 ; 9 : -0.0546311241246911 ; 10 : -4.5405897155646e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-21-4.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 0.9984696
Unnormalized w:
0 : 1 ; 1 : -0.0222488666349984 ; 2 : -3.67963458333565e-08 ; 3 : -0.0305901424996169 ; 4 : -9.91810860074905e-11 ; 5 : -0.0181738670775706 ; 6 : -1.28727999626536e-10 ; 7 : -0.00369933523612707 ; 8 : 1.84444589209588e-12 ; 9 : -0.000244215680810886 ; 10 : -4.70743787109451e-15 ;
Normalized w:
0 : 1 ; 1 : -0.0222488666349984 ; 2 : -5.20378913233036e-08 ; 3 : -0.0749302402830873 ; 4 : -4.85886105706888e-10 ; 5 : -0.199084739109718 ; 6 : -3.45413469327003e-09 ; 7 : -0.262626748816313 ; 8 : 3.70361795765185e-10 ; 9 : -0.147114358550837 ; 10 : -8.96739114182644e-12 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-21-5.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.00472727695854174 ; 2 : -1.65233452512046e-07 ; 3 : -0.00871970234241137 ; 4 : -7.26175856188191e-09 ; 5 : -0.00384432022731011 ; 6 : 3.96221835275131e-10 ; 7 : -0.000970206415293238 ; 8 : -2.5922457234301e-11 ; 9 : -0.000116338829610484 ; 10 : 1.44348638780645e-13 ;
Normalized w:
0 : 1 ; 1 : 0.00472727695854174 ; 2 : -2.33675389500266e-07 ; 3 : -0.0213588214478591 ; 4 : -3.55752062237953e-08 ; 5 : -0.0421124181354227 ; 6 : 1.0631747494139e-08 ; 7 : -0.0688778227073985 ; 8 : -5.20518810179489e-09 ; 9 : -0.0700819547535723 ; 10 : 2.74975632219082e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-21-6.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : 0.0108754693780752 ; 2 : -2.93278647895105e-09 ; 3 : 0.00353567356114553 ; 4 : 4.41653225137319e-09 ; 5 : 0.00135438461270386 ; 6 : -9.53123097490072e-10 ; 7 : 0.000501786037775442 ; 8 : 1.31469423502094e-11 ; 9 : 5.21440900672862e-05 ; 10 : -3.73013804233255e-13 ;
Normalized w:
0 : 1 ; 1 : 0.0108754693780752 ; 2 : -4.147586414077e-09 ; 3 : 0.00866059612185564 ; 4 : 2.16365008968194e-08 ; 5 : 0.014836540078316 ; 6 : -2.55749764429555e-08 ; 7 : 0.0356232748022994 ; 8 : 2.63988507253635e-09 ; 9 : 0.0314113505610895 ; 10 : -7.10569268348634e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-21-7.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 1
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 0.9978326
Unnormalized w:
0 : 1 ; 1 : 0.0196032252483651 ; 2 : 1.91789565403605e-07 ; 3 : -0.00513778634181481 ; 4 : -2.39821350258084e-08 ; 5 : -0.00170055627190666 ; 6 : -1.6507373024075e-09 ; 7 : -0.000620376748796571 ; 8 : 7.07028696197817e-11 ; 9 : -8.23539419523238e-05 ; 10 : -1.43905493238789e-12 ;
Normalized w:
0 : 1 ; 1 : 0.0196032252483651 ; 2 : 2.71231404515421e-07 ; 3 : -0.0125849549448869 ; 4 : -1.17487987511518e-07 ; 5 : -0.0186286606086033 ; 6 : -4.42939298541335e-08 ; 7 : -0.0440423800975256 ; 8 : 1.41970235453092e-08 ; 9 : -0.0496096209064922 ; 10 : -2.74131466132265e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-21-8.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.00722137943819359 ; 2 : 1.84856711876845e-07 ; 3 : -0.00167198383292764 ; 4 : -5.18706981932582e-08 ; 5 : 0.000950107383682747 ; 6 : -5.0267900036921e-10 ; 7 : 0.000424305135351643 ; 8 : 2.99813721087855e-11 ; 9 : 2.38144849516342e-05 ; 10 : -9.44569375784918e-13 ;
Normalized w:
0 : 1 ; 1 : -0.00722137943819359 ; 2 : 2.6142686903193e-07 ; 3 : -0.00409550724885557 ; 4 : -2.54113486350776e-07 ; 5 : 0.0104079049219051 ; 6 : -1.34882929882463e-08 ; 7 : 0.0301226763974304 ; 8 : 6.02021174017547e-09 ; 9 : 0.0143457318803013 ; 10 : -1.79934887834958e-09 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-21-9.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Number of False Discoveries by BH at FDR = 0.05: 0
Number of False Discoveries by ASH at lfsr = 0.05: 0
pihat0 estimated by ASH: 1
Unnormalized w:
0 : 1 ; 1 : -0.00748162680537013 ; 2 : -3.31075201234638e-08 ; 3 : -0.00508832201391876 ; 4 : -9.34529107037692e-09 ; 5 : 0.000527168441275429 ; 6 : -3.15048135566165e-13 ; 7 : -0.000521174978479096 ; 8 : -1.99161817334975e-12 ; 9 : -6.02561900317788e-06 ; 10 : 1.48913603391889e-13 ;
Normalized w:
0 : 1 ; 1 : -0.00748162680537013 ; 2 : -4.68211039751427e-08 ; 3 : -0.0124637925810718 ; 4 : -4.5782389240423e-08 ; 5 : 0.0057748409378278 ; 6 : -8.45362856772617e-12 ; 7 : -0.0369997530436507 ; 8 : -3.99913755302532e-10 ; 9 : -0.00362980407965978 ; 10 : 2.83671620214799e-10 ; </code></pre>
<p><img src="figure/mosek_reg_4.rmd/unnamed-chunk-21-10.png" width="672" style="display: block; margin: auto;" /></p>
</div>
</div>
<div id="session-information" class="section level2">
<h2>Session information</h2>
<pre class="r"><code>sessionInfo()</code></pre>
<pre><code>R version 3.4.3 (2017-11-30)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS High Sierra 10.13.4
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRlapack.dylib
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] Rmosek_8.0.69 PolynomF_1.0-1 CVXR_0.95 REBayes_1.2
[5] Matrix_1.2-12 SQUAREM_2017.10-1 EQL_1.0-0 ttutils_1.0-1
loaded via a namespace (and not attached):
[1] Rcpp_0.12.16 knitr_1.20 whisker_0.3-2
[4] magrittr_1.5 workflowr_1.0.1 bit_1.1-12
[7] lattice_0.20-35 R6_2.2.2 stringr_1.3.0
[10] tools_3.4.3 grid_3.4.3 R.oo_1.21.0
[13] git2r_0.21.0 scs_1.1-1 htmltools_0.3.6
[16] bit64_0.9-7 yaml_2.1.18 rprojroot_1.3-2
[19] digest_0.6.15 gmp_0.5-13.1 ECOSolveR_0.4
[22] R.utils_2.6.0 evaluate_0.10.1 rmarkdown_1.9
[25] stringi_1.1.6 Rmpfr_0.6-1 compiler_3.4.3
[28] backports_1.1.2 R.methodsS3_1.7.1</code></pre>
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