Sur les estimateurs du maximum de vraisemblance dans les modèles multiplicatifs de Poisson et binomiale négative

Abstract

We are interested in the existence and uniqueness of maximum likelihood estimators of parameters in the two multiplicative regression models, with Poisson or negative binomial probability distributions. Following its work on the multiplicative Poisson model with two factors without repeated measures, Haberman gave a necessary and sufficient condition for existence and uniqueness of the maximum likelihood estimator of this model, furthermore, he provided an explicit expression of this estimator. In this paper, we propose a generalization of these results to a multiplicative Poisson model with repeated measures and more than two factors. We also show that the condition obtained is also a necessary and sufficient condition for the existence and uniqueness of the maximum likelihood estimator in the multiplicative negative binomial model with several factors, with or without repeated measures.