On Kendall's regression

Journal article (2020)

Authors

Alexis Derumigny University of Twente
Jean David Fermanian CREST-ENSAE
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Conditional Kendall's tau Kernel smoothing Conditional dependence measures Regression-type models
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Published Date

2020-7

Language

English

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Abstract

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 and a two-step inference procedure. We prove non-asymptotic bounds with explicit constants that hold with high probabilities. We derive the consistency of the latter estimator, its asymptotic law and some oracle properties. Some simulations and applications to real data conclude the paper.