Marčenko-pastur law for Kendall’s tau

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,…,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.