English

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.

Keywords

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}
}
R2 v1 2026-06-24T06:25:45.974Z