Robust Fits for Copula Models

In this paper we obtain robust estimators for copula parameters through the minimization of weighted goodness of ̄t statistics. Di®erent weight functions emphasize di®erent regions on the unit square and are able to handle di®erent locations of model violation. The resultingWMDE estimators are compared to the classical maximum likelihood estimatorsMLE, and to their weighted version WMLE, an estimator obtained in two steps. The weights obtained in the ̄rst step by the application of a high breakdown point scatter matrix estimator are used to identify atypical points. All estimators are compared in a comprehensive simulation study. For each 2-contaminated parametric copula family considered, we showed that there is a robust estimator improving over the MLE and able to capture the correct strength of dependence of the data, despite the contamination percentual and location, and the sample size.