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Minimum volume confidence regions for a multivariate normal mean vector. (English) Zbl 1110.62077

Summary: Since C. Stein’s original proposal [ibid. 24, 265–285 (1962; Zbl 0126.34602)], 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.

MSC:

62H12 Estimation in multivariate analysis
62F25 Parametric tolerance and confidence regions
62F15 Bayesian inference

Citations:

Zbl 0126.34602
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References:

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