A multivariate correlation ratio

Allan R. Sampson

Statistics & Probability Letters, 1984, vol. 2, issue 2, 77-81

Abstract: A multivariate correlation ratio of a random vector Y upon a random vector X is defined by [eta][delta] (Y;X)={tr([delta]-1 CovE(YX))}1/2 {tr([delta]-1 [summation operator]Y)}-1/2 where [Lambda], a fixed positive definite matrix, is related to the relative importance of predictability for the entries of Y. The properties of [eta][Lambda] are discussed, with particular attention paid to a 'correlation-maximizing' property. Given are applications of [eta][Lambda] to the elliptically symmetric family of distributions and the multinomial distribution. Also discussed is the problem of finding those r linear functions of Y that are most predictable (in a correlation ratio sense) from X.

Keywords: correlation; ratio; multivariate; correlation; ratio; vector; correlation; elliptically; symmetric (search for similar items in EconPapers)
Date: 1984
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