Date of this Version
The Annals of Statistics
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.
multivariate normal mean, volume, coverage probability, confidence sets, James-Stein estimator, pseudo-empirical-Bayes construction
Tseng, Y., & Brown, L. D. (1997). Good Exact Confidence Sets for a Multivariate Normal Mean. The Annals of Statistics, 25 (5), 2228-2258. http://dx.doi.org/10.1214/aos/1069362396
Date Posted: 27 November 2017
This document has been peer reviewed.