Marčenko-pastur law for Kendall’s tau

Afonso S. Bandeira; Asad Lodhia; Philippe Rigollet

doi:10.1214/17-ECP59

Marčenko-pastur law for Kendall’s tau

Afonso S. Bandeira, Asad Lodhia, Philippe Rigollet

Mathematics

Research output: Contribution to journal › Article › peer-review

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 X₁,…,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.

Original language	English (US)
Article number	32
Journal	Electronic Communications in Probability
Volume	22
DOIs	https://doi.org/10.1214/17-ECP59
State	Published - 2017

Keywords

Random matrix theory
Statistics

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/17-ECP59

Cite this

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abstract = "We prove that Kendall{\textquoteright}s Rank correlation matrix converges to the Mar{\v c}enko Pastur law, under the assumption that observations are i.i.d random vectors X1,…,Xn 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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AU - Lodhia, Asad

AU - Rigollet, Philippe

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N2 - 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 X1,…,Xn 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.

AB - 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 X1,…,Xn 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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KW - Statistics

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JO - Electronic Communications in Probability

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ER -

Marčenko-pastur law for Kendall’s tau

Abstract

Keywords

ASJC Scopus subject areas

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