The Annals of Statistics
- Ann. Statist.
- Volume 10, Number 3 (1982), 868-881.
Minimax Confidence Sets for the Mean of a Multivariate Normal Distribution
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.
Ann. Statist. Volume 10, Number 3 (1982), 868-881.
First available in Project Euclid: 12 April 2007
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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.