# Estimation of copulas via Maximum Mean Discrepancy

@article{Alquier2022EstimationOC,
title={Estimation of copulas via Maximum Mean Discrepancy},
author={Pierre Alquier and Badr-Eddine Ch'erief-Abdellatif and A. Derumigny and Jean-David Fermanian},
journal={Journal of the American Statistical Association},
year={2022}
}
• Published 1 October 2020
• Computer Science, Mathematics
• Journal of the American Statistical Association
This paper 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 non-asymptotic 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…
3 Citations

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## References

SHOWING 1-10 OF 50 REFERENCES
Robust Estimation of Bivariate Copulas
• Computer Science, Economics
• 2013
A bounded-bias robust estimator that is corrected for consistency by means of indirect inference is proposed and in a simulation study it is shown that the robust estimators outperform the popular approaches.
Robust Fits for Copula Models
• Mathematics
Commun. Stat. Simul. Comput.
• 2007
It is shown that there is a robust estimator improving over the MLE and able to capture the correct strength of dependence of the data, despite the contamination percentual and location, and the sample size.
Semiparametric estimation in copula models
The author recalls the limiting behaviour of the empirical copula process and applies it to prove some asymptotic properties of a minimum distance estimator for a Euclidean parameter in a copula
Statistical Inference for Generative Models with Maximum Mean Discrepancy
• Computer Science, Mathematics
ArXiv
• 2019
Theoretical properties of a class of minimum distance estimators for intractable generative models, that is, statistical models for which the likelihood is intracted, but simulation is cheap, are studied, showing that they are consistent, asymptotically normal and robust to model misspecification.
MMD-Bayes: Robust Bayesian Estimation via Maximum Mean Discrepancy
• Mathematics, Computer Science
AABI
• 2019
A pseudo-likelihood based on the Maximum Mean Discrepancy, defined via an embedding of probability distributions into a reproducing kernel Hilbert space is built, and it is shown that this MMD-Bayes posterior is consistent and robust to model misspecification.
Subsampling (weighted smooth) empirical copula processes
• Computer Science, Mathematics
J. Multivar. Anal.
• 2019
A new method for estimation and model selection:$$\rho$$ρ-estimation
• Mathematics
• 2017
The aim of this paper is to present a new estimation procedure that can be applied in various statistical frameworks including density and regression and which leads to both robust and optimal (or
Weak convergence of the empirical copula process with respect to weighted metrics
• Mathematics
• 2014
The empirical copula process plays a central role in the asymptotic analysis of many statistical procedures which are based on copulas or ranks. Among other applications, results regarding its weak