Correlations of functions of normal variables

Sam Gutmann

Journal of Multivariate Analysis, 1978, vol. 8, issue 4, 573-578

Abstract: Let (X1, X2,..., Xk, Y1, Y2,..., Yk) be multivariate normal and define a matrix C by Cij = cov(Xi, Yj). If (i) (X1,..., Xk) = (Y1,..., Yk) and (ii) C is symmetric positive definite, then 0 corr(f(X1,..., Xk),f(Y1,..., Yk)) > 0. Condition (i) is necessary for the conclusion. The sufficiency of (i) and (ii) follows from an infinite-dimensional version, which can also be applied to a pair of jointly normal Brownian motions.

Keywords: Correlation; functions; of; normal; variables (search for similar items in EconPapers)
Date: 1978
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