Maximum likelihood estimation and large-sample inference for generalized linear and nonlinear regression models

Abstract

The class of generalized linear models is extended to allow for correlated observations, nonlinear models and error distributions not of the exponential family form. The extended class of models include a number of important examples, particularly of the composite transformational type. Large-sample inference and maximum likelihood estimation for the extended class of generalized linear models are discussed, and the analysis of deviance is generalized to the extended class of models. Calculation of the maximum likelihood estimate for a general likelihood by Fisher's scoring method and a related method is considered, and the relation with the Gauss–Newton method is discussed.