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Minimax Confidence Sets for the Mean of a Multivariate Normal Distribution

Jiunn Tzon Hwang and George Casella
The Annals of Statistics
Vol. 10, No. 3 (Sep., 1982), pp. 868-881
Stable URL: http://www.jstor.org/stable/2240910
Page Count: 14
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Minimax Confidence Sets for the Mean of a Multivariate Normal Distribution
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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 ≥ 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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