The Annals of Statistics
- Ann. Statist.
- Volume 47, Number 6 (2019), 3504-3532.
Tracy–Widom limit for Kendall’s tau
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.
Ann. Statist., Volume 47, Number 6 (2019), 3504-3532.
Received: March 2018
Revised: August 2018
First available in Project Euclid: 31 October 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Primary: 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52) 62G10: Hypothesis testing
Secondary: 62H10: Distribution of statistics 15B52: Random matrices 62H25: Factor analysis and principal components; correspondence analysis
Bao, Zhigang. Tracy–Widom limit for Kendall’s tau. Ann. Statist. 47 (2019), no. 6, 3504--3532. doi:10.1214/18-AOS1786. https://projecteuclid.org/euclid.aos/1572487401
- Supplement to “Tracy–Widom limit for Kendall’s tau”. The supplement includes the proofs of some technical lemmas and some additional simulation studies.