## Electronic Communications in Probability

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

### Marčenko-Pastur law for Kendall’s tau

Afonso S. Bandeira, Asad Lodhia, and Philippe Rigollet

#### 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