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

09/28/2021

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by   Zeng Li, et al.

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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 Marc̆enko-Pastur law which is a brand new limiting spectral distribution for sample covariance/correlation matrices. 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 of Kendall's rank correlation matrix and its connections with the sample covariance/correlation matrix.