Extreme Nonlinear Correlation for Multiple Random Variables and Stochastic Processes with Applications to Additive Models.

The maximum correlation of functions of a pair of random variables is an important measure of stochastic dependence. It is known that this maximum nonlinear correlation is identical to the absolute value of the Pearson correlation for a pair of Gaussian random variables or a pair of nested sums of iid square integrable random variables. This paper extends these results to pairwise Gaussian processes and vectors, nested sums of iid random variables, and permutation symmetric functions of sub-groups of iid random variables.