Mar\v{c}enko-Pastur Law for Kendall's Tau

Afonso S. Bandeira; Asad Lodhia; Philippe Rigollet

Mar\v{c}enko-Pastur Law for Kendall's Tau

Statistics Theory 2017-01-24 v2 Probability Statistics Theory

Authors: Afonso S. Bandeira , Asad Lodhia , Philippe Rigollet

Abstract

We prove that Kendall's Rank correlation matrix converges to the Mar\v{c}enko-Pastur law, under the assumption that the observations are i.i.d random vectors $X_1$ , $\dots$ , $X_n$ 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.

Keywords

Kendall's tau Marčenko-Pastur law random matrix theory empirical spectral distribution U-statistics rank correlation

Cite

@article{arxiv.1611.04505,
  title  = {Mar\v{c}enko-Pastur Law for Kendall's Tau},
  author = {Afonso S. Bandeira and Asad Lodhia and Philippe Rigollet},
  journal= {arXiv preprint arXiv:1611.04505},
  year   = {2017}
}

Comments

Fixed errors and typos in the section 3

Mar\v{c}enko-Pastur Law for Kendall's Tau

Abstract

Keywords

Cite

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