Open Access
2017 Marčenko-Pastur law for Kendall’s tau
Afonso S. Bandeira, Asad Lodhia, Philippe Rigollet
Electron. Commun. Probab. 22: 1-7 (2017). DOI: 10.1214/17-ECP59


We prove that Kendall’s Rank correlation matrix converges to the Marčenko Pastur law, under the assumption that observations are i.i.d random vectors $X_1, \ldots , X_n$ with components that are independent and absolutely continuous with respect to the Lebesgue measure. This is the first result on the empirical spectral distribution of a multivariate $U$-statistic.


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Afonso S. Bandeira. Asad Lodhia. Philippe Rigollet. "Marčenko-Pastur law for Kendall’s tau." Electron. Commun. Probab. 22 1 - 7, 2017.


Received: 25 January 2017; Accepted: 15 May 2017; Published: 2017
First available in Project Euclid: 3 June 2017

zbMATH: 1366.60007
MathSciNet: MR3663103
Digital Object Identifier: 10.1214/17-ECP59

Primary: 60B20 , 62H20

Keywords: Random matrix theory , statistics

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