Package asus. October 25, 2017
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1 Package asus October 25, 2017 Title Aaptive SURE Thresholing Using Sie Information Version Provies the ASUS proceure for estimating a high imensional sparse parameter in the presence of auxiliary ata that encoe sie information on sparsity. It is a robust ata combination proceure in the sense that even when pooling noninformative auxiliary ata ASUS woul be at least as efficient as competing soft thresholing base methos that o not use auxiliary ata. For more information, please see the website < an the accompanying paper. Depens R (>= 3.4.2) License GPL (>= 2) Encoing UTF-8 LazyData true URL Imports rwt, wavethresh, stats, utils RoxygenNote Suggests knitr, rmarkown VignetteBuiler knitr NeesCompilation no Author Trambak Banerjee [aut, cre], Gourab Mukherjee [aut], Wenguang Sun [aut] Maintainer Trambak Banerjee <trambakb@usc.eu> Repository CRAN Date/Publication :45:32 UTC R topics ocumente: asus asus.cuts
2 2 asus ejs sureshrink sureshrink.mse Inex 7 asus Aaptive SURE thresholing with sie information (asus) ASUS proceure for shrinkage estimation of a high imensional sparse parameter. asus(,, s, k = 2, m = 50) s an n vector of primary observations an n vector of variances for each component of an n vector of sie information k number of groups. Default is k=2 m partitions the support of s into m equiistant points. Default is m = 50 Estimates a sparse high imensional vector using the ASUS proceure escribe in Banerjee et al. (2017). If k = 1 then ASUS is the SureShrink estimator. The current implementation of ASUS estimates the grouping threshols base on the magnitue of s. See the reference for more etails. 1. est - an n vector holing the estimates 2. mse - estimate of risk 3. tau - k-1 vector of grouping parameters if k>=2 4. t - k vector of thresholing parameters 5. size - k vector of group sizes Banerjee. T, Mukherjee. G an Sun. W (2017). Aaptive Sparse Estimation with Sie Information. sureshrink,ejs,sureshrink.mse
3 asus.cuts 3 <-rnorm(10,2,1) <- rep(1,10) s<-rnorm(10,3,0.1) asus.out<-asus(,,s) asus.cuts Risk of asus with pre-efine grouping threshols Estimates the risk of asus when there are k(>2) groups with pre-efine grouping threshols asus.cuts(,, s, cutpoints) an n vector of primary observations an n vector of variances for each component of s an n vector of sie information cutpoints k-1 pre-efine grouping threshols for k groups. k must be bigger than 2. Estimates the risk of asus when there are k(>2) groups with k pre-efine grouping threshols. This function is calle when asus executes. mse - estimate of risk Banerjee. T, Mukherjee. G an Sun. W (2017). Aaptive Sparse Estimation with Sie Information. asus,sureshrink,ejs,sureshrink.mse
4 4 ejs <-rnorm(10) <- rep(1,10) s<-rnorm(10) out<-asus.cuts(,,s,c(0.1,0.5,1)) ejs Extene James-Stein (ejs) estimator Extene James-Stein estimator of a high imensional sparse parameter. ejs(, ) an n vector of observations an n vector of variances for each component of Extene James-Stein estimator of mean from Brown (2008) an equation (7.3) in Xie et al. (2012) est - an n vector holing the estimates 1. Brown, L.D. (2008). In-Season Preiction of Batting Averages: A Fiel Test of Empirical Bayes an Bayes Methoologies. The Annals of Applie Statistics, 2, Xie, X. C., Kou, S. C., an Brown, L. D. (2012). SURE Estimates for a Heterosceastic Hierarchical Moel. Journal of the American Statistical Association, 107, sureshrink,asus
5 sureshrink 5 <-rnorm(10,2,1) <- rep(1,10) theta.hat<-ejs(,) sureshrink SureShrink estimator SureShrink estimator of a high imensional sparse parameter from Donoho an Johnstone (1995) sureshrink(, ) an n vector of observations an n vector of variances for each component of Estimates a threshol t by minimizing the SURE function an then soft threshols using t. 1. est - an n vector holing the estimates 2. t - estimate threshol Davi L Donoho an Iain M Johnstone. Aapting to unknown smoothness via wavelet shrinkage. Journal of the american statistical association, 90(432): , 1995 sureshrink.mse <-rnorm(10,2,1) <- rep(1,10) theta.hat<-sureshrink(,)
6 6 sureshrink.mse sureshrink.mse SURE estimate of risk Stein s Unbiase Risk Estimate for the sureshrink estimator sureshrink.mse(,, type = 1, t = 0) type an n vector of observations an n vector of variances for each component of set type=1 if you want the thresholing parameter t to be estimate. Otherwise set type = 0 in which case you must provie t. Default is type = 1 t soft thresholing parameter. If type = 1, then t is estimate whereas if type = 0 then you must provie t. Default is t = 0 (an type = 1) Estimates the risk of the surehsrink estimator of Donoho an Johnstone (1995). 1. sure.est - SURE estimate of risk 2. t - estimate threshol (meaningless if type = 0) 1. Charles M Stein. Estimation of the mean of a multivariate normal istribution. The annals of Statistics, pages , Davi L Donoho an Iain M Johnstone. Aapting to unknown smoothness via wavelet shrinkage. Journal of the american statistical association, 90(432): , 1995 sureshrink,asus <-rnorm(10,2,1) <- rep(1,10) mse<-sureshrink.mse(,)
7 Inex asus, 2, 3, 4, 6 asus.cuts, 3 ejs, 2, 3, 4 sureshrink, 2 4, 5, 6 sureshrink.mse, 2, 3, 5, 6 7
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