An Orthogonally Invariant Minimax Estimator of the Covariance Matrix of a Multivariate Normal Population

Abstract

In the problem of estimating the covariance matrix of a multivariate normal population James and Stein obtained a minimax estimator by considering the best invariant estimator with respect to the triangular group. In this paper its authors propose an orthogonally invariant estimator obtained by averaging the minimax estimator with respect to the invariant measure on the orthogonal group. Explicit forms of the proposed estimator are given for dimensions 2 and 3. Risk is evaluated for various population covariance matrices and it shows a substantial improvement over the minimax estimator for a wide range of population covariance matrices.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1983
Accession Number
ADA128843

Entities

People

  • Akimichi Takemura

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Computing-Related Activities
  • Covariance
  • Data Science
  • Estimators
  • Information Science
  • Mathematics
  • Statistical Algorithms
  • Statistical Analysis

Fields of Study

  • Mathematics

Readers

  • Statistical inference.