  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 finite sums of
iid random variables. This paper extends these results to pairwise Gaussian
vectors and processes, nested sums of iid random variables, and permutation
symmetric functions of sub-groups of iid random variables. It also discusses
applications to additive regression models.
