Maximum Likelihood Estimation of the Parameters of a Multivariate Normal Distribution

Abstract

This paper provides an exposition of several altnerative techniques used to obtain maximum likelihood estimators for the parameters of a multivariate normal distribution. In particular, matrix differentiation, matrix transformations and induction are treated. These techniques are used to derive the maximum likelihood estimators of the covariances of a Wishart distribution, of the covariances when there are missing observations, and of the means under a rank constraint. Although the paper is mainly expository, some of the proofs are new.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1979
Accession Number
ADA073796

Entities

People

  • I. Olkin
  • Theodore W. Anderson

Organizations

  • Stanford University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Analysis Of Variance
  • Confidence Limits
  • Covariance
  • Data Science
  • Distribution Functions
  • Estimators
  • Inequalities
  • Information Science
  • Maximum Likelihood Estimation
  • Multivariate Analysis
  • Normal Distribution
  • Observation
  • Statistical Algorithms
  • Statistical Analysis
  • Statistical Inference
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Statistical inference.