Bias correction in power series generalized nonlinear models

Abstract

Power series generalized nonlinear models [Comput. Statist. Data Anal. 53 (2009) 1155–1166] can be used when the Poisson assumption of equidispersion is not valid. In these models, we consider a more general family of discrete distributions for the response variable and a nonlinear structure for the regression parameters, although the dispersion parameter and other shape parameters are assumed known. We derive a general matrix formula for the second-order bias of the maximum likelihood estimate of the regression parameter vector in these models. We use the results by [J. Roy. Statist. Soc. B 30 (1968) 248–275] and bootstrap technique [Ann. Statist. 7 (1979) 1–26] to obtain the bias-corrected maximum likelihood estimate. Simulation studies are performed using different estimates. We also present an empirical application.