28.01.2019 16:00 Jean-David Fermanian:
On Kendall's regressionBC1 2.02.01 (Parkring 11, 85748 Garching)

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. We show how the problem of estimating conditional Kendall's tau can be rewritten as a classification task. We detail specific algorithms 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, we apply all these estimators to a dataset of European stock indices.