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

TL;DR

This paper investigates nonparametric methods for estimating conditional Kendall's tau, providing finite-sample bounds, consistency proofs, asymptotic laws, and simulation results to evaluate estimator performance.

Contribution

It introduces explicit finite-sample bounds and direct proofs for the consistency and asymptotic behavior of nonparametric estimators of conditional Kendall's tau.

Findings

Finite-sample bounds with explicit constants

Proofs of consistency and asymptotic law

Simulation study demonstrating estimator performance

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.