Statistics Papers

Document Type

Journal Article

Date of this Version

11-2014

Publication Source

Journal of Statistical Planning and Inference

Volume

154

Start Page

62

Last Page

71

DOI

10.1016/j.jspi.2014.02.010

Abstract

Detecting significance in a high-dimensional sparse data structure has received a large amount of attention in modern statistics. In the current paper, we introduce a compound decision rule to simultaneously classify signals from noise. This procedure is a Bayes rule subject to a mixture loss function. The loss function minimizes the number of false discoveries while controlling the false nondiscoveries by incorporating the signal strength information. Based on our criterion, strong signals will be penalized more heavily for nondiscovery than weak signals. In constructing this classification rule, we assume a mixture prior for the parameter which adapts to the unknown sparsity. This Bayes rule can be viewed as thresholding the “local fdr” (Efron, 2007) by adaptive thresholds. Both parametric and nonparametric methods will be discussed. The nonparametric procedure adapts to the unknown data structure well and outperforms the parametric one. Performance of the procedure is illustrated by various simulation studies and a real data application.

Copyright/Permission Statement

© 2014. This manuscript version is made available under the CC-BY-NC-ND 4.0 license.

Keywords

high dimensional sparse inference, Bayes classification rule, nonparametric estimation, false discoveries, false nondiscoveries

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Date Posted: 27 November 2017

This document has been peer reviewed.