Title

Rates Of Convergence Of Empirical Bayes Tests For A Normal Mean

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. © 2002 Elsevier Science B.V. All rights reserved.

Publication Date

2-1-2003

Publication Title

Journal of Statistical Planning and Inference

Volume

111

Issue

1-2

Number of Pages

181-196

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/S0378-3758(02)00300-2

Socpus ID

0037290170 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0037290170

This document is currently not available here.

Share

COinS