The Asymptotic Theory Of Generalized Linear Models

The theory of generalized linear models (GLM) is an extension of the class-ical theory of linear models. As for a statistical model, it has been widely used and deeply applied to many fields, such as Biology, Medicine, Economy and Social science, statistical analysis. It provides a set of regression analysis meth-ods and many effective models for practical application in statistics, for examp-le, logistic regression model, log-linear model, probit model and so on. The generalized linear model mainly includes modeling, statistical analysis, model selection and diagnosis, etc..This thesis consists of four parts as follows:In chapter 1, we briefly introduce the research background and the present situation of GLM.In chapter 2, we study the consistency of maximum quasi-likelihood estim-ation(MQLE) of GLM. On the one hand, we prove the strong consistency of MQLE of GLM with unnatural link function under mild conditions. On the oth-er hand, we use a fixed-point theorem to prove the weak consistency. The inde-pendent sequence is extended to dependency sequence.In chapter 3 and chapter 4, the asymptotic theory of GLM is used to stud-y generalized estimating equations(GEE). The strong consistency of GEE root is studied when some smoothness conditions are met. The results show that the st- rong consistency not only existences in the martingale difference sequence amo-ng subjects, but also existences in the dependent sequence for multidimension-al case. These two results are essential improvements over the related results in the literature.