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arXiv · 2109.13624

On eigenvalues of a high-dimensional Kendall's rank correlation matrix with dependence

Zeng Li·Cheng Wang·Qinwen Wang
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Abstract

This paper investigates limiting spectral distribution of a high-dimensional Kendall's rank correlation matrix. The underlying population is allowed to have general dependence structure. The result no longer follows the generalized Mar\u{c}enko-Pastur law, which is brand new. It's the first result on rank correlation matrices with dependence. As applications, we study the Kendall's rank correlation matrix for multivariate normal distributions with a general covariance matrix. From these results, we further gain insights on Kendall's rank correlation matrix and its connections with the sample covariance/correlation matrix.

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Zeng Li, Cheng Wang, Qinwen Wang. 2021-09-28. On eigenvalues of a high-dimensional Kendall's rank correlation matrix with dependence. https://arxiv.org/abs/2109.13624

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