Copula-based regression estimation in the presence of outliers

Ordinary least square estimators for linear regression models are highly influenced by outliers. Copula is a powerful tool for studying the dependence between response and predictor variables and may overcome several limitations associated with the classical linear regression models. In this study, we investigate the efficacy of the copula-based regression models over classical linear regression in the presence of outliers in the x, y, and x-y directions. We also examine the performance of several robust regression estimation techniques when variables are related via elliptical and Archimedean family of copulas and outliers are present in the data. Finally, real and artificial data sets are analyzed to compare the performance of various robust regression techniques.