The Annals of Statistics

Minimax Confidence Sets for the Mean of a Multivariate Normal Distribution

Jiunn Tzon Hwang and George Casella

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

First available in Project Euclid: 12 April 2007

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

Confidence sets Stein estimation multivariate normal density minimax estimation


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.

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