Improved estimators for generalized linear models with dispersion covariates

Abstract

This paper addresses the issue of bias reduction of maximum likelihood estimators in generalized linear models with dispersion covariates. For this class of models, we derive general formulae for the second-order biases of maximum likelihood estimators of the linear and dispersion parameters, linear predictors, precision parameters and mean values. Our formulae cover many important and commonly used models and can be viewed as an extension of the results in Cordeiro and McCullagh (1991) and Cordeiro (1993)These formulae are easily implemented by means of supplementary weighted linear regressions. They are also simple enough to be used algebraically to obtain several closed-form expressions in special models. The practical use of such bias corrections is illustrated in a simulation study.