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This paper is concerned with the limiting spectral behaviors of largedimensional Kendall's rank correlation matrices generated by samples withindependent and continuous components. We do not require the components to beidentically distributed, and do not need any moment conditions, which is verydifferent from the assumptions imposed in the literature of random matrixtheory. The statistical setting in this paper covers a wide range of highlyskewed and heavy-tailed distributions. We establish the central limit theorem(CLT) for the linear spectral statistics of the Kendall's rank correlationmatrices under the Marchenko-Pastur asymptotic regime, in which the dimensiondiverges to infinity proportionally with the sample size. We further proposethree nonparametric procedures for high dimensional independent test and theirlimiting null distributions are derived by implementing this CLT. Our numericalcomparisons demonstrate the robustness and superiority of our proposed teststatistics under various mixed and heavy-tailed cases.

Central Limit Theorem for Linear Spectral Statistics of Large Dimensional Kendall's Rank Correlation Matrices and its Applications