Nonnormal Multivariate Distributions: Inference Based on Elliptically Contoured Distributions

Abstract

The class of elliptically contoured distributions, which includes multivariate t-distributions and contaminated normal distributions, serves as a useful generalization of the class of normal multivariate distributions. The density, marginal and conditional densities, and moments of an elliptically contoured distribution are related in a simple fashion to those of a normal distribution. The asymptotic normal distributions of the sample mean and covariance matrix are developed and are compared with the asymptotic distributions of the maximum likelihood estimators of the parameters of an elliptically contoured distribution. The class of elliptically contoured distributions serves as a model for evaluating other robust estimators. Many test procedures for normal distributions are easily modified for the elliptically contoured distributions. Further generalizations are discussed.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1992
Accession Number
ADA254999

Entities

People

  • Theodore W. Anderson

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Correlation Analysis
  • Covariance
  • Data Analysis
  • Data Mining
  • Data Science
  • Distribution Theory
  • Estimators
  • Information Science
  • Maximum Likelihood Estimation
  • Military Research
  • Multivariate Analysis
  • New York
  • Normal Distribution
  • Statistical Algorithms
  • Statistical Analysis
  • Statistical Inference
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Statistical inference.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms