Tracy–Widom limit for Kendall’s tau
The Annals of Statistics · 2019 · Volume 47 · Issue 6
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.
Keywords
15B52, 60B20, 62G10, 62H10, 62H25, Largest eigenvalue, nonparametric statistics, random matrices, Tracy–Widom law, U-statistics
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