Parametric Robust Inferences for Regression Parameters under Generalized Linear Models

Abstract

Parametric robust likelihood functions for regression parameters are introduced in the setting of generalized linear models. It is demonstrated that ordinary normal regression (ONR) models and gamma regression models, when properly adjusted, provide asymptotically valid inferences for regression parameters for practically all nonnegative continuous response variables (NCRVs). It is demonstrated that the adjusted robust gamma regression is superior to the adjusted robust normal regression in many respects for the analysis of NCRVs. The connection between the novel robust regression models and the estimating equations approach is also provided.