Estimation of Copulas via Maximum Mean Discrepancy
本文提出基于最大均值差异原则的参数连接函数模型估计方法，该方法在存在异常值或模型设定错误时仍保持稳健，并适用于无密度函数的连接函数（如Marshall-Olkin连接函数），模拟研究显示其优于伪极大似然估计。
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 [0,1]d, 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.