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arXiv · 1611.04505

Marčenko-Pastur Law for Kendall's Tau

Afonso S. Bandeira·Asad Lodhia·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 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.

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Afonso S. Bandeira, Asad Lodhia, Philippe Rigollet. 2017-01-21. Marčenko-Pastur Law for Kendall's Tau. https://arxiv.org/abs/1611.04505

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