Robust Poisson regression

Count data are very often analyzed under the assumption of a Poisson model [(Agresti, A., 1996. An Introduction to Categorical Data Analysis. Wiley, New York; Generalized Linear Models, second ed. Chapman & Hall, New York)]. However, the derived inference is generally erroneous if the underlying distribution is not Poisson (Biometrika 70, 269-274). A parametric robust regression approach is proposed for the analysis of count data. More specifically it will be demonstrated that the Poisson regression model could be properly adjusted to become asymptotically valid for inference about regression parameters, even if the Poisson assumption fails. With large samples the novel robust methodology provides legitimate likelihood functions for regression parameters, so long as the true underlying distributions have finite second moments. Adjustments that robustify the Poisson regression will be given, respectively, under log link and identity link functions. Simulation studies will be used to demonstrate the efficacy of the robust Poisson regression model.