Electronic Communications in Probability

Marčenko-Pastur law for Kendall’s tau

Afonso S. Bandeira, Asad Lodhia, and Philippe Rigollet

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1496455233

Digital Object Identifier
doi:10.1214/17-ECP59

Mathematical Reviews number (MathSciNet)
MR3663103

Zentralblatt MATH identifier
1366.60007

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

Keywords
statistics random matrix theory

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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