Robust regression against heavy heterogeneous contamination

Abstract

The gamma -divergence is well-known for having strong robustness against heavy contamination. By virtue of this property, many applications via the gamma -divergence have been proposed. There are two types of gamma -divergence for the regression problem, in which the base measures are handled differently. In this study, these two gamma -divergences are compared, and a large difference is found between them under heterogeneous contamination, where the outlier ratio depends on the explanatory variable. One gamma -divergence has the strong robustness even under heterogeneous contamination. The other does not have in general; however, it has under homogeneous contamination, where the outlier ratio does not depend on the explanatory variable, or when the parametric model of the response variable belongs to a location-scale family in which the scale does not depend on the explanatory variables. Hung et al. (Biometrics 74(1):145–154, 2018) discussed the strong robustness in a logistic regression model with an additional assumption that the tuning parameter gamma is sufficiently large. The results obtained in this study hold for any parametric model without such an additional assumption.