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The maximum correlation of functions of a pair of random variables is animportant measure of stochastic dependence. It is known that this maximumnonlinear correlation is identical to the absolute value of the Pearsoncorrelation for a pair of Gaussian random variables or a pair of finite sums ofiid random variables. This paper extends these results to pairwise Gaussianvectors and processes, nested sums of iid random variables, and permutationsymmetric functions of sub-groups of iid random variables. It also discussesapplications to additive regression models.

Extreme Eigenvalues of Nonlinear Correlation Matrices with Applications to Additive Models