Statistics Papers

Document Type

Journal Article

Date of this Version

1997

Publication Source

The Annals of Statistics

Volume

25

Issue

5

Start Page

2228

Last Page

2258

DOI

10.1214/aos/1069362396

Abstract

A class of confidence sets with constant coverage probability for the mean of a p-variate normal distribution is proposed through a pseudo-empirical-Bayes construction. When the dimension is greater than 2, by combining analytical results with some exact numerical calculations the proposed sets are proved to have a uniformly smaller volume than the usual confidence region. Sufficient conditions for the connectedness of the proposed confidence sets are also derived. In addition, our confidence sets could be used to construct tests for point null hypotheses. The resultant tests have convex acceptance regions and hence are admissible by Birnbaum. Tabular results of the comparison between the proposed region and other confidence sets are also given.

Keywords

multivariate normal mean, volume, coverage probability, confidence sets, James-Stein estimator, pseudo-empirical-Bayes construction

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Date Posted: 27 November 2017

This document has been peer reviewed.