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December 2019 Tracy–Widom limit for Kendall’s tau
Zhigang Bao
Ann. Statist. 47(6): 3504-3532 (December 2019). DOI: 10.1214/18-AOS1786

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.

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Zhigang Bao. "Tracy–Widom limit for Kendall’s tau." Ann. Statist. 47 (6) 3504 - 3532, December 2019. https://doi.org/10.1214/18-AOS1786

Information

Received: 1 March 2018; Revised: 1 August 2018; Published: December 2019
First available in Project Euclid: 31 October 2019

Digital Object Identifier: 10.1214/18-AOS1786

Subjects:
Primary: 60B20, 62G10
Secondary: 15B52, 62H10, 62H25

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 6 • December 2019
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