Minimax Estimation of a Multivariate Normal Mean with Unknown Covariance Matrix.

Abstract

Let X be a p-variate (p>or=3) vector, normally distributed with unknown mean theta and unknown covariance matrix sigma. Let W:pXp be distributed independently of X, and let W have a Wishart distribution with n degrees of freedom and parameter sigma. It is desired to estimate theta under the quadratic loss (delta-theta)'Q(delta-theta), where Q is a known positive definite matrix. Under the condition that a lower bound for the smallest characteristic root of Q sigma is known, a family of minimax estimators is developed.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1976
Accession Number
ADA037531

Entities

People

  • Leon Jay Gleser

Organizations

  • Purdue University

Tags

DTIC Thesaurus Topics

  • Air Force
  • Computing-Related Activities
  • Covariance
  • Data Science
  • Estimators
  • Information Science
  • Interdisciplinary Science
  • Mathematical Analysis
  • Normal Distribution
  • Scientific Research
  • Square Roots
  • Statistical Analysis
  • Statistics
  • Theorems
  • Universities

Fields of Study

  • Mathematics

Readers

  • Statistical inference.