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Minimum volume confidence regions for a multivariate normal mean vector
Author(s) -
Efron Bradley
Publication year - 2006
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2006.00560.x
Subject(s) - multivariate statistics , multivariate normal distribution , volume (thermodynamics) , mathematics , confidence interval , statistics , multivariate analysis , normal distribution , bayes' theorem , bayesian probability , physics , quantum mechanics
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.