Invariant Tests and Likelihood Ratio Tests for Multivariate Elliptically Contoured Distributions

Abstract

The usual assumption in multivariate hypothesis testing is that the sample consists of n independent, identically distributed Gaussian p-vectors. In this dissertation this assumption is weakened by considering a class of distributions for which the vector observation are not necessarily Gaussian or independent. The following hypothesis testing problems are considered: testing for equality between the mean vector and a specified vector, lack of correlations among different sets, equality of covariance matrices and mean vectors, equality between the correlation coefficient and a specified number, and MANOVA. For each of the above hypotheses, invariant tests and their properties are developed. These include the uniformly most powerful test, the locally most powerful test, admissibility, and null and non-null distributions. Keywords include: Invariant test; likelihood ratio test; multivariate elliptically contoured distribution; admissibility locally most powerful invariant test; maximal invariant; maximum likelihood estimation.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1985
Accession Number
ADA155844

Entities

People

  • H. Hsu
  • Theodore W. Anderson

Organizations

  • Stanford University

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Asymptotic Normality
  • Bessel Functions
  • Covariance
  • Data Science
  • Information Science
  • Insensitive Explosives
  • Maximum Likelihood Estimation
  • Military Research
  • Multivariate Analysis
  • Normal Distribution
  • Normality
  • Probability
  • Regression Analysis
  • Statistical Algorithms
  • Statistical Analysis
  • Statistical Inference
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Statistical inference.