Accession Number : AD0714814

Title :   Proper Bayes Minimax Estimators of the Multivariate Normal Mean.

Descriptive Note : Technical rept.,

Corporate Author : STANFORD UNIV CALIF DEPT OF STATISTICS

Personal Author(s) : Strawderman,William E.

Report Date : 02 NOV 1970

Pagination or Media Count : 11

Abstract : Consider the problem of estimating the mean of a multivariate normal distribution with covariance matrix the identity and sum of squared errors loss. It is shown that there exist proper Bayes minimax estimators when the dimension is greater than or equal to 5. This answers, partially, a conjecture in the folklore attributed to Charles Stein to the effect that in 3 and 4 dimensions proper Bayes minimax estimators do not exist, while they do in dimensions greater than or equal to 5. In 1 and 2 dimensions, of course, (x bar) is unique minimax and is not proper Bayes. (Author)

Descriptors :   (*STATISTICAL DISTRIBUTIONS, DECISION THEORY), MINIMAX TECHNIQUE, MULTIVARIATE ANALYSIS, THEOREMS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE