Statistics Papers

Document Type

Journal Article

Date of this Version

2009

Publication Source

Annals of Statistics

Volume

37

Issue

4

Start Page

1685

Last Page

1704

DOI

10.1214/08-AOS630

Abstract

We consider the classical problem of estimating a vector μ=(μ1, …, μn) based on independent observations YiN(μi, 1), i=1, …, n.

Suppose μi, i=1, …, n are independent realizations from a completely unknown G. We suggest an easily computed estimator μ̂, such that the ratio of its risk E(μ̂μ)2 with that of the Bayes procedure approaches 1. A related compound decision result is also obtained.

Our asymptotics is of a triangular array; that is, we allow the distribution G to depend on n. Thus, our theoretical asymptotic results are also meaningful in situations where the vector μ is sparse and the proportion of zero coordinates approaches 1.

We demonstrate the performance of our estimator in simulations, emphasizing sparse setups. In “moderately-sparse” situations, our procedure performs very well compared to known procedures tailored for sparse setups. It also adapts well to nonsparse situations.

Keywords

empirical Bayes, compound decision

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Date Posted: 27 November 2017

This document has been peer reviewed.