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.

中文翻译：

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非线性相关矩阵的极值特征及其在加性模型中的应用

一对随机变量的函数的最大相关性是随机依赖的重要度量。众所周知，对于一对高斯随机变量或一对iid随机变量的有限和，该最大非线性相关性与皮尔逊相关性的绝对值相同。本文将这些结果扩展到成对的高斯向量和过程，iid随机变量的嵌套和，以及iid随机变量的子组的置换对称函数。它还讨论了加性回归模型的应用。