Robust Fits for Copula Models

Abstract

In this article, we obtain robust estimators for copula parameters through the minimization of weighted goodness-of-fit statistics. Different weight functions emphasize different regions on the unit square and are able to handle different locations of model violation. The resulting WMDE estimators are compared to the classical maximum likelihood estimators MLE, and to their weighted version WMLE, an estimator obtained in two steps. The weights obtained in the first 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 ∊-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.

Keywords:

• ∊-Contaminated distributions
• Empirical copula
• Minimum distance estimators
• Robust estimation

Mathematics Subject Classification:

• Primary 62F35
• Secondary 62F10, 62P05

Acknowledgment

The authors gratefully acknowledge Brazilian financial support from FAPERJ, CNPq, CAPES, and COPPEAD research grants.

Notes

Notation in table: SS–Sample size.