Generalized Linear Model Of The Maximum Likelihood Estimation Consistency And Asymptotic Normality

Generalized linear models are used for regression analysis, which is dependent on linear combination Z 0. Generalized linear models can be able to used to many linear model in practice. The responses of generalized linear models belong to a natural exponential family which can be handled easily in mathematics processes. Consistency is the basic and deeply-research sample property. So the study of the consistency of maximum likelihood estimate of generalized linear models and its asymptotic normality is fundamental to deduce reasonably and analysis deeply for the data collecting from practical problems and abstract model. The thesis aims to the study of maximum likelihood estimate of generalized linear models and its asymptotic normality. We mainly discuss the structures of generalized linear models, the set-up of the practice models, the choice of the link function and consistency and asymptotic normality.We arrange the thesis as follows:1. In Chapter 1, we first introduce the structure of generalized linear models and basic concepts we may use following chapters. First, we focus on some characteristics of natural exponential family and examples. Secondly, we introduce the dummy variable and two way of taking its value, which is very important for the study of the generalized linear model with discrete responses.2. In Chapter 2, we discuss several concrete generalized linear models in a systemic way. Briefly on the set-up of the models and the choices of link function.3. In Chapter 3, we introduce the methods of studying maximum likelihood estimate, and use them to the generalized linear models.4. In Chapter 4, we discuss and prove the consistency and asymptotic normality of maximum likelihood estimate to the exponential models.