On bias reduction in exponential and non-exponential family regression models

This paper addresses the issue of bias reduction of maximum likelihood estimators in generalized linear models and non-exponential family nonlinear regression models. We study both the bias of the estimators of the parameters in the linear predictors and of the means. We also consider the bias of the estimator of the precision parameter at different regions of the parameter space. Simple formulae are given for some special cases. The finite-sample behavior of maximum likelihood estimators and their bias-corrected counterparts is compared through simulation. Our results cover a number of important and commonly used models.