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

In this paper, we investigate the limiting spectral distribution of a high-dimensional Kendall’s rank correlation matrix. The underlying population is allowed to have a general dependence structure. The result no longer follows the generalized Marc̆enko-Pastur law, which is brand new. It is the first result on rank correlation matrices with dependence. As applications, we study Kendall’s rank correlation matrix for multivariate normal distributions with a general covariance matrix. From these results, we further gain insights into Kendall’s rank correlation matrix and its connections with the sample covariance/correlation matrix.