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) : Strawderman,William E.

Report Date : 04 JAN 1971

Pagination or Media Count : 13

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)

Descriptors :   (*STATISTICAL DISTRIBUTIONS, DECISION THEORY), MULTIVARIATE ANALYSIS, MATHEMATICAL PREDICTION, NUMERICAL INTEGRATION, INEQUALITIES, THEOREMS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE