About Kendall's regression

Conditional Kendall's tau is a measure of dependence between two random variables, conditionally on some covariates. We study nonparametric estimators of such quantities using kernel smoothing techniques. Then, we assume a regression-type relationship between conditional Kendall's tau and covariates, in a parametric setting with possibly a large number of regressors. This model may be sparse, and the underlying parameter is estimated through a penalized criterion. The theoretical properties of all these estimators are stated. We prove non-asymptotic bounds with explicit constants that hold with high probability. We derive their consistency, their asymptotic law and some oracle properties. Some simulations and applications to real data conclude the paper.