Translator Disclaimer
September, 1982 Minimax Confidence Sets for the Mean of a Multivariate Normal Distribution
Jiunn Tzon Hwang, George Casella
Ann. Statist. 10(3): 868-881 (September, 1982). DOI: 10.1214/aos/1176345877

Abstract

For the problem of estimating a $p$-variate normal mean, the existence of confidence procedures which dominate the usual one, a sphere centered at the observations, has long been known. However, no explicit procedure has yet been shown to dominate. For $p \geq 4$, we prove that if the usual confidence sphere is recentered at the positive-part James Stein estimator, then the resulting confidence set has uniformly higher coverage probability, and hence is a minimax confidence set. Moreover, the increase in coverage probability can be quite substantial. Numerical evidence is presented to support this claim.

Citation

Download Citation

Jiunn Tzon Hwang. George Casella. "Minimax Confidence Sets for the Mean of a Multivariate Normal Distribution." Ann. Statist. 10 (3) 868 - 881, September, 1982. https://doi.org/10.1214/aos/1176345877

Information

Published: September, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0508.62031
MathSciNet: MR663438
Digital Object Identifier: 10.1214/aos/1176345877

Subjects:
Primary: 62C20
Secondary: 62F25

Rights: Copyright © 1982 Institute of Mathematical Statistics

JOURNAL ARTICLE
14 PAGES


SHARE
Vol.10 • No. 3 • September, 1982
Back to Top