The Annals of Statistics
- Ann. Statist.
- Volume 25, Number 5 (1997), 2228-2258.
Good exact confidence sets for a multivariate normal mean
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.
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
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. https://projecteuclid.org/euclid.aos/1069362396