Minimum volume confidence regions for a multivariate normal mean vector

Bradley Efron

Journal of the Royal Statistical Society Series B, 2006, vol. 68, issue 4, 655-670

Abstract: Summary. Since Stein's original proposal in 1962, a series of papers have constructed confidence regions of smaller volume than the standard spheres for the mean vector of a multivariate normal distribution. A general approach to this problem is developed here and used to calculate a lower bound on the attainable volume. Bayes and fiducial methods are involved in the calculation. Scheffé‐type problems are used to show that low volume by itself does not guarantee favourable inferential properties.

Date: 2006
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