Title

Rates of convergence of empirical Bayes tests for a normal mean

Authors

Authors

M. Pensky

Comments

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Abbreviated Journal Title

J. Stat. Plan. Infer.

Keywords

PARAMETER EXPONENTIAL FAMILY; GEOMETRIZING RATES; Statistics & Probability

Abstract

In the present paper, the EB two-action problem under the linear error loss is considered for the family of normal distributions with the location parameter. The purpose is to establish the upper and lower bounds for the risk. A monotone adaptive empirical Bayes test is constructed with the regret risk converging to zero at a rate of O(n(-1)(ln n)(3/2)). The lower bound for the risk of the form O(n(-1)(ln n)(1/2)(ln ln n)(-1)) is derived. In the author's opinion, the (ln n ln ln n) times difference between the lower and the upper bounds is due not to the fact that the estimator suggested in the paper is not optimal but to the fact that the lower bound is not exact. (C) 2002 Elsevier Science B.V. All rights reserved.

Journal Title

Journal of Statistical Planning and Inference

Volume

111

Issue/Number

1-2

Publication Date

1-1-2003

Document Type

Article; Proceedings Paper

Language

English

First Page

181

Last Page

196

WOS Identifier

WOS:000180324200013

ISSN

0378-3758

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