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

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 firs...

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Bibliographic Details
Published inarXiv.org
Main Authors Zeng, Li, Wang, Cheng, Wang, Qinwen
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 31.08.2022
Subjects
Correlation analysis
Eigenvalues
Entropy
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Summary: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.
ISSN:2331-8422