Some Inference Problems Associated with the Complex Multivariate Normal Distribution

Abstract

Consider k = q+1 complex multivariate normal populations with the same variance-covariance matrix but with different means. The problem of the number of discriminant functions needed to discriminate among the k-populations is considered and shown to be equivalent to the rank of the mean-space. A test for this dimensionality being R is presented. Also developed is the statistic for testing the goodness of fit of a single hypothetical discriminant function. As in the case of the real normal populations, the test statistic for this single hypothetical function is presented as the product of two independent factors, whose distributions are given; one measuring the direction aspect of the hypothetical function, and the other measures the collinearity aspect that is the necessity of only one function. Also included is the Bartlett decomposition of a complex Wishart matrix and some results pertaining to the coherence of complex random variables.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1971
Accession Number
AD0735454

Entities

People

  • John C. Young

Organizations

  • Southern Methodist University

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Analysis Of Variance
  • Data Science
  • Decomposition
  • Gaussian Processes
  • Information Science
  • Multivariate Analysis
  • New York
  • Normal Distribution
  • Probability
  • Probability Density Functions
  • Random Variables
  • Regression Analysis
  • Statistical Algorithms
  • Statistical Analysis
  • Statistical Inference
  • Vector Spaces
  • Wishart Matrices

Fields of Study

  • Mathematics

Readers

  • Regression Analysis.
  • Statistical inference.

Technology Areas

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