## The Annals of Statistics

### A Robust Generalized Bayes Estimator and Confidence Region for a Multivariate Normal Mean

James Berger

#### Abstract

It is observed that in selecting an alternative to the usual maximum likelihood estimator, $\delta^0$, of a multivariate normal mean, it is important to take into account prior information. Prior information in the form of a prior mean and a prior covariance matrix is considered. A generalized Bayes estimator is developed which is significantly better than $\delta^0$ if this prior information is correct and yet is very robust with respect to misspecification of the prior information. An associated confidence region is also constructed, and is shown to have very attractive size and probability of coverage.

#### Article information

Source
Ann. Statist., Volume 8, Number 4 (1980), 716-761.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176345068

Digital Object Identifier
doi:10.1214/aos/1176345068

Mathematical Reviews number (MathSciNet)
MR572619

Zentralblatt MATH identifier
0464.62026

JSTOR