Nonparametric Empirical Bayes Estimation for Sparse, Heteroskedastic Normal Means

• Activity Number: 119
• Type: Topic Contributed
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Linda Zhao*
• Companies: University of Pennsylvania
• Keywords: Nonparametric Empirical Bayes ; Heteroskedasticity ; Sparse means ; Multiple testing ; FDR

Abstract

We consider the normal means problem where the variances may not be the same. The goal is to make inferences for the unknown means. Also in modern data analyses, we often run into the situation that a large number of hypotheses need to be tested simultaneously. Yet only a few of the alternatives hypotheses are believed to be true.

We propose to use Bayesian nonparametric schemes to tackle the problem. The method lends itself especially well for adapting to varying degrees of sparsity. It performs well to estimate the means. It also provides credible intervals. We also propose a method to control FDR in the case of multiple testing.

Joint work with D. McCarthy and Y. Ritov