论文标题
通过最大平均差异估计Copulas
Estimation of copulas via Maximum Mean Discrepancy
论文作者
论文摘要
本文介绍了参数copula模型的强大推断。使用规范最大似然的估计可能是不稳定的，尤其是在存在异常值的情况下。我们建议使用基于最大平均差异（MMD）原理的程序。我们得出了该新估计量的非反应性甲骨文不平等，一致性和渐近正态性。特别是，甲骨文的不平等在库氏家族上没有任何假设，并且可以在存在异常值或错误指定的情况下应用。此外，在我们的MMD框架中，与Marshall-Olkin Copula一样，相对于$ [0,1]^d $的Lebesgue度量没有密度的Copula模型的统计推断，这变得可行。一项模拟研究表明了我们的新程序的鲁棒性，尤其是与伪最大的可能性估计相比。可以使用实现MMD估计器的R软件包。
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 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.
