A multivariate correlation ratio |
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Authors: | Allan R Sampson |
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Affiliation: | Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, PA 15260, USA |
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Abstract: | A multivariate correlation ratio of a random vector upon a random vector is defined by where Λ, a fixed positive definite matrix, is related to the relative importance of predictability for the entries of . The properties of ηΛ are discussed, with particular attention paid to a ‘correlation-maximizing’ property. Given are applications of ηΛ to the elliptically symmetric family of distributions and the multinomial distribution. Also discussed is the problem of finding those r linear functions of that are most predictable (in a correlation ratio sense) from . |
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Keywords: | 62H20 62J05 correlation ratio multivariate correlation ratio vector correlation elliptically symmetric |
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