On eigenvalues of a high-dimensional Kendall's rank correlation matrix with dependence
Statistics Theory
2022-09-01 v3 Statistics Theory
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.
Cite
@article{arxiv.2109.13624,
title = {On eigenvalues of a high-dimensional Kendall's rank correlation matrix with dependence},
author = {Zeng Li and Cheng Wang and Qinwen Wang},
journal= {arXiv preprint arXiv:2109.13624},
year = {2022}
}