Nonnegative Definiteness of the Estimated Dispersion Matrix in a Multivariate Linear Model

Abstract

Estimation is considered in model where both the mean vector and the dispersion matrix have linear decompositions. It is shown that after an invariance reduction with respect to mean translation, MINQUE provides a nonnegative definite estimate of the dispersion matrix, when the decomposing matrices span a quadratic subspace of symmetric matrices. With normality, MINQUE is seen to equal the restricted maximum likelihood estimate and to be of uniformly minimum variance.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1978
Accession Number
ADA060864

Entities

People

  • Friedrich Pukelsheim
  • George P. H. Styan

Organizations

  • Stanford University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algebra
  • Covariance
  • Data Science
  • Equations
  • Estimators
  • Information Science
  • Invariance
  • Mathematics
  • Maximum Likelihood Estimation
  • Normality
  • Probability
  • Random Variables
  • Statistical Algorithms
  • Statistical Analysis
  • Statistical Inference
  • Statistics
  • United States

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Reinforced Composite Materials
  • Statistical inference.