Tracy-Widom limit for Kendall's tau

Abstract

In this paper, we study a high-dimensional random matrix model from nonparametric statistics called the Kendall rank correlation matrix, which is a natural multivariate extension of the Kendall rank correlation coefficient. We establish the Tracy-Widom law for its largest eigenvalue. It is the first Tracy-Widom law for a nonparametric random matrix model, and also the first Tracy-Widom law for a high-dimensional U-statistic.

supplementary material is attached to the end of the paper for the convenience of the reader

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• Lectures on the local semicircle law for Wigner matrices
• The Tracy--Widom limit for the largest eigenvalues of singular complex Wishart matrices
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