### Abstract

Original language | English |
---|---|

Pages (from-to) | 70-94 |

Number of pages | 25 |

Journal | Computational statistics & data analysis |

Volume | 135 |

Early online date | 5 Feb 2019 |

DOIs | |

Publication status | Published - 1 Jul 2019 |

Externally published | Yes |

### Keywords

- Conditional Kendall's tau
- Conditional dependence measure
- Machine learning
- Classification task
- Stock indices

### Cite this

*Computational statistics & data analysis*,

*135*, 70-94. https://doi.org/10.1016/j.csda.2019.01.013

}

*Computational statistics & data analysis*, vol. 135, pp. 70-94. https://doi.org/10.1016/j.csda.2019.01.013

**A classification point-of-view about conditional Kendall's tau.** / Derumigny, Alexis; Fermanian, Jean-David.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - A classification point-of-view about conditional Kendall's tau

AU - Derumigny, Alexis

AU - Fermanian, Jean-David

PY - 2019/7/1

Y1 - 2019/7/1

N2 - 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 ) 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.

AB - 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 ) 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.

KW - Conditional Kendall's tau

KW - Conditional dependence measure

KW - Machine learning

KW - Classification task

KW - Stock indices

U2 - 10.1016/j.csda.2019.01.013

DO - 10.1016/j.csda.2019.01.013

M3 - Article

VL - 135

SP - 70

EP - 94

JO - Computational statistics & data analysis

JF - Computational statistics & data analysis

SN - 0167-9473

ER -