A classification point-of-view about conditional Kendall's tau

It is shown how the problem of estimating conditional Kendall's tau can be rewritten as a classification task. Conditional Kendall's tau is a conditional dependence parameter that is a characteristic of a given pair of random variables. The goal is to predict whether the pair is concordant (value of 1) or discordant (value of −1) conditionally on some covariates. The consistency and the asymptotic normality of a family of penalized approximate maximum likelihood estimators is proven, including the equivalent of the logit and probit regressions in our framework. Specific algorithms are detailed, adapting usual machine learning techniques, including nearest neighbors, decision trees, random forests and neural networks, to the setting of the estimation of conditional Kendall's tau. Finite sample properties of these estimators and their sensitivities to each component of the data-generating process are assessed in a simulation study. Finally, all these estimators are applied to a dataset of European stock indices.