smash-gen with unknown variance

Last updated: 2018-05-17

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From the comparisons for estimating unknown \(\sigma\), the ols and smash verison of method 4 perform uniformly better. To deal with case when both \(\mu_t\) and \(\sigma\) are unknown in the model \(Y_t=\mu_t+N(0,\sigma^2)+N(0,s_t^2)\), we adopt the iterative algorithm in Xing\(\&\)Stephens(2016). We initialize \(\hat\sigma^2=\frac{1}{T}\Sigma_t^T\{((Y_t-Y_{t+1})^2+(Y_t-Y_{t+1})^2-2s_t^2-s_{t-1}^2-s_{t+1}^2)/4\}\).

#' function to estimate both mu and \sigma

#' @param x:data
#' @param st: known variance
#' @param family: wavelet basis
#' @param filter.number: as in smash.gaus
#' @param niters: number of iterations to estimate \sigma and mu
#' @param y_var_est: 'mle', 'moment', 'eb', 'huber','wls'
#' @param z_var_est: method to estimate variance: 'rmad', 'smash', 'default'
#' @param k: parameter in huber m estimator
#' @return estimated mean and \sigma
#' @export

smash.gaus.gen=function(x,st,y_var_est='mle',z_var_est='smash',family='DaubExPhase',
                        filter.number=1,niters=2,k=NULL){
  #initialize \sigma^2 using moment method
  sigma0=sigma_est(x,st=st,method = 'moment')
  #sd0=sqrt(sigma0^2+st^2)
  sd.est=c()
  mu.est=c()
  sd.est=c(sd.est,sigma0)
  for(iter in 1:niters){
    #estimate mu given sd
    mu.hat=smash.gaus(x,sigma=sqrt(sd.est[iter]^2+st^2),family=family,filter.number = filter.number)
    mu.est=rbind(mu.est,mu.hat)
    #estimate sd given mu
    sd.hat=sigma_est(x,mu.est[iter,],st,var_est=z_var_est,k=k,method=y_var_est,family=family,filter.number = filter.number)
    sd.est=c(sd.est,sd.hat)
  }
  #mu.hat=smash.gaus(x,sigma=sqrt(sd.hat^2+st^2),family=family)
  return(list(mu.hat=mu.hat,sd.hat=sd.hat))
}

sessionInfo()

R version 3.4.0 (2017-04-21)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 16299)

Matrix products: default

locale:
[1] LC_COLLATE=English_United States.1252 
[2] LC_CTYPE=English_United States.1252   
[3] LC_MONETARY=English_United States.1252
[4] LC_NUMERIC=C                          
[5] LC_TIME=English_United States.1252    

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

loaded via a namespace (and not attached):
 [1] workflowr_1.0.1   Rcpp_0.12.16      digest_0.6.13    
 [4] rprojroot_1.3-2   R.methodsS3_1.7.1 backports_1.0.5  
 [7] git2r_0.21.0      magrittr_1.5      evaluate_0.10    
[10] stringi_1.1.6     whisker_0.3-2     R.oo_1.21.0      
[13] R.utils_2.6.0     rmarkdown_1.8     tools_3.4.0      
[16] stringr_1.3.0     yaml_2.1.19       compiler_3.4.0   
[19] htmltools_0.3.5   knitr_1.20       

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