On kernel-based estimation of conditional Kendall's tau: finite-distance bounds and asymptotic behavior

Abstract

We study nonparametric estimators of conditional Kendall's tau, a measure of concordance between two random variables given some covariates. We prove non-asymptotic bounds with explicit constants, that hold with high probabilities. We provide "direct proofs" of the consistency and the asymptotic law of conditional Kendall's tau. A simulation study evaluates the numerical performance of such nonparametric estimators.

29 pages, 4 figures. arXiv admin note: text overlap with arXiv:1802.07613