Minimum volume confidence regions for a multivariate normal mean vector
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2006 · Volume 68 · Issue 4
DOI: 10.1111/j.1467-9868.2006.00560.x
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.
Keywords
Fisher–von Mises distribution, James–Stein estimator, Non-centralχ, Scheffé intervals
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