Estimation of Copulas via Maximum Mean Discrepancy

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

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
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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.

Original languageEnglish
Number of pages17
JournalJournal of the American Statistical Association
Publication statusPublished - 2022

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • Algorithms semiparametric inference
  • Copula
  • Kernel methods and RKHS
  • Robust procedures


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