About Kendall's regression.

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