Electronic Communications in Probability

Marčenko-Pastur law for Kendall’s tau

Afonso S. Bandeira, Asad Lodhia, and Philippe Rigollet

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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.

Article information

Electron. Commun. Probab. Volume 22 (2017), paper no. 32, 7 pp.

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

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Zentralblatt MATH identifier

Primary: 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52) 62H20: Measures of association (correlation, canonical correlation, etc.)

statistics random matrix theory

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Bandeira, Afonso S.; Lodhia, Asad; Rigollet, Philippe. Marčenko-Pastur law for Kendall’s tau. Electron. Commun. Probab. 22 (2017), paper no. 32, 7 pp. doi:10.1214/17-ECP59. https://projecteuclid.org/euclid.ecp/1496455233

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