Proper Bayes Minimax Estimators of the Multivariate Normal Mean.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 02, 1970
- Accession Number
- AD0714814
Entities
People
- William E. Strawderman
Organizations
- Stanford University