Specialty: Mathematics and their interactions presented by ALPHA OUMAR DIALLO DOCTORAL SCHOOLS: ED MATHSTIC and ED ST / UGB LABORATORY: IRMAR and LERSTAD ; Spécialité : Mathématiques et leurs interactions présentée par ALPHA OUMAR DIALLO ECOLES DOCTORALES : ED MATHSTIC et ED ST/UGB LABORATOIRE : IRMAR et LERSTAD

The zero-inflated regression models are a very powerful tool for the analysis of counting data with excess zeros from various areas such as epidemiology, health economics or ecology. However, the theoretical study in these models attracts little attention. This manuscript is interested in the problem of inference in zero-inflated count models. At first, we return to the question of the maximum likelihood estimator in the zero-inflated binomial model. First we show the existence of the maximum likelihood estimator of the parameters in this model. Then, we demonstrate theconsistency of this estimator, and let us establish its asymptotic normality. Then, a comprehensive simulation study finite sample sizes are conducted to evaluate the consistency of our results. Finally, an application on real health economics data has been conduct. In a second time, we propose a new statistical analysis model of the consumption of medical care. This model allows, among other things, to identify the causes of the non-use of medical care. We have studied rigorously the mathematical properties of the model. Then, we carried out an exhaustive numerical study using computer simulations and finally applied to the analysis of a database on health care several thousand patients in the USA. A final aspect of this work was to focus on the problem of inference in the zero inflation binomial model in the context of missing covariate data. In this case we propose the weighting method by the inverse of the selection probabilities to estimate the parameters of the model. Then, we establish the consistency and asymptotic normality of the estimator offers. Finally, a simulation study on several samples of finite sizes is conducted to evaluate the behavior of the estimator. ; Les modèles de régressions à inflation de zéros constituent un outil très puissant pour l’analyse de données de comptage avec excès de zéros, émanant de divers domaines tels que l’épidémiologie, l’économie de la santé ou encore l’écologie. Cependant, l’étude théorique dans ...