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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


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.


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Jiunn Tzon Hwang. George Casella. "Minimax Confidence Sets for the Mean of a Multivariate Normal Distribution." Ann. Statist. 10 (3) 868 - 881, September, 1982.


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

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

Primary: 62C20
Secondary: 62F25

Keywords: Confidence sets , minimax estimation , multivariate normal density , Stein estimation

Rights: Copyright © 1982 Institute of Mathematical Statistics


Vol.10 • No. 3 • September, 1982
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