### Abstract

Original language | English |
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Number of pages | 37 |

Publication status | Published - 20 Nov 2018 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### Cite this

*About Kendall's regression*.

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**About Kendall's regression.** / Derumigny, Alexis; Fermanian, Jean-David.

Research output: Working paper

TY - UNPB

T1 - About Kendall's regression

AU - Derumigny, Alexis

AU - Fermanian, Jean-David

PY - 2018/11/20

Y1 - 2018/11/20

N2 - 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.

AB - 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.

KW - Conditional dependence measure

KW - kernel smoothing

KW - regression-type models

KW - Conditional Kendall's tau

M3 - Working paper

BT - About Kendall's regression

ER -