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.
ALQUIER, P., CHERIEF-ABDELLATIF, B.E., DERUMIGNY, A. et FERMANIAN, J.D. (2023). Estimation of Copulas via Maximum Mean Discrepancy. Journal of the American Statistical Association, 118(543), pp. 1997-2012.