### 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. 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.

Original language | English |
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Number of pages | 37 |

Publication status | Published - 20 Nov 2018 |

Externally published | Yes |

### Keywords

- Conditional dependence measure
- kernel smoothing
- regression-type models
- Conditional Kendall's tau

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## Cite this

Derumigny, A., & Fermanian, J-D. (2018).

*About Kendall's regression*.