Estimation of Copulas via Maximum Mean Discrepancy

Estimation of Copulas via Maximum Mean Discrepancy

Alquier, Pierre (RIKEN Center for Emergent Matter Science (CEMS))
Chérief-Abdellatif, Badr Eddine (University of Oxford)
Derumigny, Alexis (TU Delft Statistics)
Fermanian, Jean David (ENSAE Paris)

2022

This article deals with robust inference for parametric copula models. Estimation using canonical maximum likelihood might be unstable, especially in the presence of outliers. We propose to use a procedure based on the maximum mean discrepancy (MMD) principle. We derive nonasymptotic oracle inequalities, consistency and asymptotic normality of this new estimator. In particular, the oracle inequality holds without any assumption on the copula family, and can be applied in the presence of outliers or under misspecification. Moreover, in our MMD framework, the statistical inference of copula models for which there exists no density with respect to the Lebesgue measure on (Formula presented.), as the Marshall-Olkin copula, becomes feasible. A simulation study shows the robustness of our new procedures, especially compared to pseudo-maximum likelihood estimation. An R package implementing the MMD estimator for copula models is available. Supplementary materials for this article are available online.

Algorithms semiparametric inference
Copula
Kernel methods and RKHS
Robust procedures

http://resolver.tudelft.nl/uuid:caf3a363-025f-4dff-b5b7-8c17820d1162

https://doi.org/10.1080/01621459.2021.2024836

2022-07-04

0162-1459

American Statistical Association. Journal

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© 2022 Pierre Alquier, Badr Eddine Chérief-Abdellatif, Alexis Derumigny, Jean David Fermanian