Consistency and asymptotic normality of the maximum likelihood estimates in reproductive dispersion linear models

Reproductive dispersion linear models (RDLMs) include generalized linear model [Nelder and Wedderburn (1972). Generalized linear models. J. Roy. Statist. Soc. Ser. A 135, 370-384] as a special case. Some mild regularity conditions analogous to those given by Fahrmeir and Kaufmann [1985. Consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models. Ann. Statist. 13, 342-368] are proposed. On the basis of the proposed mild conditions, the existence, weak consistency, strong consistency, and asymptotic normality of the maximum likelihood estimate (MLE) are provided in RDLMs. The asymptotic results of Fahrmeir and Kaufmann [1985. Consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models. Ann. Statist. 13, 342-368] are generalized to RDLMs.