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October 1997 Good exact confidence sets for a multivariate normal mean
Yu-Ling Tseng, Lawrence D. Brown
Ann. Statist. 25(5): 2228-2258 (October 1997). DOI: 10.1214/aos/1069362396


A class of confidence sets with constant coverage probability for the mean of a p-variate normal distribution is proposed through a pseudo-empirical-Bayes construction. When the dimension is greater than 2, by combining analytical results with some exact numerical calculations the proposed sets are proved to have a uniformly smaller volume than the usual confidence region. Sufficient conditions for the connectedness of the proposed confidence sets are also derived. In addition, our confidence sets could be used to construct tests for point null hypotheses. The resultant tests have convex acceptance regions and hence are admissible by Birnbaum. Tabular results of the comparison between the proposed region and other confidence sets are also given.


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Yu-Ling Tseng. Lawrence D. Brown. "Good exact confidence sets for a multivariate normal mean." Ann. Statist. 25 (5) 2228 - 2258, October 1997.


Published: October 1997
First available in Project Euclid: 20 November 2003

zbMATH: 0882.62027
MathSciNet: MR1474092
Digital Object Identifier: 10.1214/aos/1069362396

Primary: 62F25
Secondary: 62C15 , 62C20

Keywords: Confidence sets , coverage probability , James-Stein estimator , multivariate normal mean , pseudo-empirical-Bayes construction , Stein-type estimator , Volume

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 5 • October 1997
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