Inadmissibility of the Usual Estimator for the Mean of a Multivariate Normal Distribution

Abstract

If one observes the real random variables Xi, Xn independently normally distributed with unknown means xi...x in and variance 1, it is customary to estimate xi by Xi. If the loss is the sum of squares of the errors, this estimator is admissible for n < or equal to 2, but inadmissible for n more than or equal to 3. Since the usual estimator is best among those which transform correctly under translation, any admissible estimator for n equals more than or equal to 3 involves an arbitrary choice. While the results of this paper are not in a form suitable for immediate practical application, the possible improvement over the usual estimator seems to be large enough to be of practical importance if n is large.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1956
Accession Number
AD1028390

Entities

People

  • Charles Stein

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Air Force
  • California
  • Convex Sets
  • Covariance
  • Data Science
  • Estimators
  • Identities
  • Inequalities
  • Information Science
  • Military Research
  • Normal Distribution
  • Probability
  • Random Variables
  • Statistical Analysis
  • Statistics
  • United States

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Statistical inference.
  • Systems Analysis and Design