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Extreme eigenvalues of nonlinear correlation matrices with applications to additive models

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  • Guo, Zijian
  • Zhang, Cun-Hui

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.

Suggested Citation

  • Guo, Zijian & Zhang, Cun-Hui, 2022. "Extreme eigenvalues of nonlinear correlation matrices with applications to additive models," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 1037-1058.
    • Handle: RePEc:eee:spapps:v:150:y:2022:i:c:p:1037-1058
    DOI: 10.1016/j.spa.2021.04.006
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    References listed on IDEAS

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    1. Yu, Yaming, 2008. "On the maximal correlation coefficient," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1072-1075, July.
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