# 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

# Descriptors:

# Subject Categories:

- Statistics and Probability