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

Tags

DTIC Thesaurus Topics

  • Covariance
  • Data Science
  • Estimators
  • Identities
  • Information Science
  • Mathematics
  • Normal Distribution
  • Statistical Algorithms
  • Statistical Analysis

Fields of Study

  • Mathematics

Readers

  • Statistical inference.