Bias Correction in Generalized Nonlinear Models with Dispersion Covariates

Abstract

We derive general formulae for the second-order biases of maximum likelihood estimates of the parameters in generalized nonlinear models with dispersion covariates. This result generalizes previous work by Botter and Cordeiro ( 1998 Botter , D. A. , Cordeiro , G. M. ( 1998 ). Improved estimates for generalized linear models with dispersion covariates . J. Statist. Comput. Simul. 62 : 91 – 104 . [Taylor & Francis Online], [Web of Science ®] [Google Scholar] ) and Cordeiro and McCullagh ( 1991 Cordeiro , G. M. , McCullagh , P. ( 1991 ). Bias correction in generalized linear models . J. Roy Statist. Soc. B 53 : 629 – 643 . [Google Scholar] ). The practical use of such bias corrections is illustrated in a simulation study.