The Annals of Statistics

Minimax Confidence Sets for the Mean of a Multivariate Normal Distribution

Jiunn Tzon Hwang and George Casella

Full-text: Open access

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.

Article information

Source
Ann. Statist. Volume 10, Number 3 (1982), 868-881.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176345877

Digital Object Identifier
doi:10.1214/aos/1176345877

Mathematical Reviews number (MathSciNet)
MR663438

Zentralblatt MATH identifier
0508.62031

JSTOR
links.jstor.org

Subjects
Primary: 62C20: Minimax procedures
Secondary: 62F25: Tolerance and confidence regions

Keywords
Confidence sets Stein estimation multivariate normal density minimax estimation

Citation

Hwang, Jiunn Tzon; Casella, George. Minimax Confidence Sets for the Mean of a Multivariate Normal Distribution. Ann. Statist. 10 (1982), no. 3, 868--881. doi:10.1214/aos/1176345877. http://projecteuclid.org/euclid.aos/1176345877.


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