Extreme eigenvalues of nonlinear correlation matrices with applications to additive models

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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.

Original languageEnglish (US)
JournalStochastic Processes and their Applications
DOIs
StateAccepted/In press - 2021

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

Keywords

  • Additive model
  • Compatibility condition
  • Extreme eigenvalue
  • Gaussian copula
  • Nonlinear correlation
  • Restricted eigenvalue

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