Robust goodness-of-fit test for copulas by the maximum mean discrepancy estimator

Abstract

This paper discusses the robustness of suitability tests using the empirical copula process. It compares the empirical copula with a parametric estimate of the copula obtained under the null hypothesis. Fitting tests using Kendall inversion and maximum likelihood estimation methods may be less effective, especially at the sight of outliers. We recommend to establish a goodness-of-fit procedure with the Maximum Mean Discrepancy (MMD) estimator, a robust estimator, in order to assess the empirical size and power of the test under several families of alternative copulas. Then a comparative large-scale simulation study on contaminated and uncontaminated data samples is conducted to analyze the power and also the robustness of test. This approach using the MMD estimator may offer a valid alternative for goodness-of-fit tests. It is also robust in the presence of perturbations and outliers in the observations of joint distributions.