Consistency and Asymptotic Normality of the Maximum Likelihood Estimator in Exponential Family Nonlinear Models

This paper proposes some regularity conditions which weaken those given by Zhu \& Wei (1997). On the basis of the proposed regularity conditions, the existence, the strong consistency and the asymptotic normality of maximum likelihood estimation (MLE) are proved in exponential family nonlinear models (EFNMs). Our results may be regarded as a further improvement of the work of Zhu \& Wei (1997).