  Conditional Kendall's tau is a measure of dependence between two random
variables, conditionally on some covariates. We assume a regression-type
relationship between conditional Kendall's tau and some covariates, in a
parametric setting with a large number of transformations of a small number of
regressors. This model may be sparse, and the underlying parameter is estimated
through a penalized criterion. We prove non-asymptotic bounds with explicit
constants that hold with high probabilities. We derive the consistency of a
two-step estimator, its asymptotic law and some oracle properties. Some
simulations and applications to real data conclude the paper.
