Estimation of Copulas via Maximum Mean Discrepancy

• 成果类型: Article
• 署名作者: Alquier, Pierre; Cherief-Abdellatif, Badr-Eddine; Derumigny, Alexis; Fermanian, Jean-David
• 署名单位: RIKEN; University of Oxford; Delft University of Technology; Institut Polytechnique de Paris; ENSAE Paris
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2021.2024836
• 发表日期: 2023
• 页码: 1997-2012
• 关键词: WEAK-CONVERGENCE; semiparametric estimation; model selection; parameter; tests

摘要

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. for this article are available online.