Maximum likelihood estimation in misspecified generalized linear models

Abstract

Summary, This paper deals with the asymptotic behaviour of the (quasi-)maximum likelihood estimator in misspecified generalized linear models. Misspecification may be due to incorrect densities, wrong link functions, omitted regressors etc. It is shown that (quasi-Consistency and asymptotic normality can be obtained under conditions which permit substantial heterogeneity of the observations, The results are based on a general theorem on asymptotic inference under misspecification for i.n.i.d. observations, using full matrix normalization and avoiding domination or convergence conditions. For important subclasses of generalized linear models, admissible heterogeneity is characterized more explicitly in terms of the regressors