A Multivariate Correlation Ratio.
PITTSBURGH UNIV PA INST FOR STATISTICS AND APPLICATIONS
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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 BYX over suitable matrices B is considered and the results that are obtained are related to canonical correlations for the multivariate normal.
- Statistics and Probability