Accession Number:

AD0716958

Title:

On the Existence of Proper Bayes Minimax Estimators of the Mean of a Multivariate Normal Distribution.

Descriptive Note:

Technical rept.,

Corporate Author:

STANFORD UNIV CALIF DEPT OF STATISTICS

Personal Author(s):

Report Date:

1971-01-04

Pagination or Media Count:

13.0

Abstract:

Consider the problem of estimating the mean of a multivariate normal distribution with covariance matrix the identity and sum of squared errors loss. In an earlier paper the author showed that if the dimension p is 5 or greater, then proper Bayes minimax estimators do exist. This result is reviewed briefly. The main purpose of the present paper is to show for p equal to 3 or 4, that there do not exist spherically symmetric proper Bayes minimax estimators. The author has been unable, thus far, to disprove the existence of a nonspherical proper Bayes minimax estimator for p equal 3 or 4. Of course, for p 1,2, the usual estimator X bar is unique minimax but not proper Bayes. Bounds are derived for the possible bias of a minimax estimator. This result should be of some interest independent of its use in proving the main result of the paper. Author

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE