Extreme Eigenvalues of Nonlinear Correlation Matrices with Applications to Additive Models

Abstract

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.

References in corpus (6)

• Simultaneous analysis of Lasso and Dantzig selector
• Basic Properties of Strong Mixing Conditions. A Survey and Some Open Questions
• On the conditions used to prove oracle results for the Lasso
• High-dimensional additive modeling
• Sparsity in multiple kernel learning
• Fast learning rate of multiple kernel learning: Trade-off between sparsity and smoothness