A Multivariate Correlation Ratio.

Abstract

A brief review of the historical background and certain known results concerning the univariate correlation ratio are given. A multivariate correlation ratio of a random vector Y upon a random vector X is defined, where A is a given positive definite matrix. The properties of ETA sub A are discussed, with particular attention paid to a 'correlation-maximizing' property. A number of examples illustrating the application of ETA sub A are given; these examples include the multivariate normal, the elliptically symmetric distributions, the Farlie-Morgenstern-Gumbel family, and the multinomial. The problem of maximizing ETA sub A (BY;X) over suitable matrices B is considered and the results that are obtained are related to canonical correlations for the multivariate normal.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1980
Accession Number
ADA089763

Entities

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  • Allan R. Sampson

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  • University of Pittsburgh

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  • Mathematics

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  • Analytical Mechanics
  • Statistical inference.