The Annals of Statistics

Good exact confidence sets for a multivariate normal mean

Yu-Ling Tseng and Lawrence D. Brown

Full-text: Open access


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.

Article information

Ann. Statist., Volume 25, Number 5 (1997), 2228-2258.

First available in Project Euclid: 20 November 2003

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F25: Tolerance and confidence regions
Secondary: 62C20: Minimax procedures 62C15: Admissibility

Multivariate normal mean volume coverage probability confidence sets James-Stein estimator Stein-type estimator pseudo-empirical-Bayes construction


Tseng, Yu-Ling; Brown, Lawrence D. Good exact confidence sets for a multivariate normal mean. Ann. Statist. 25 (1997), no. 5, 2228--2258. doi:10.1214/aos/1069362396.

Export citation