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A multivariate correlation ratio

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  • Sampson, Allan R.

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.

Suggested Citation

  • Sampson, Allan R., 1984. "A multivariate correlation ratio," Statistics & Probability Letters, Elsevier, vol. 2(2), pages 77-81, March.
    • Handle: RePEc:eee:stapro:v:2:y:1984:i:2:p:77-81
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    Cited by:

    1. Tamás F. Móri & Gábor J. Székely, 2019. "Four simple axioms of dependence measures," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(1), pages 1-16, January.

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