Strong Consistency In Cumulative-Sequential Logit Two Stage Models

Generalized Linear models are a important generalization of classical Linear models. it is more flexible and widerly used. In this article,we are committed to strong consistency of the maximum likelihood estimator in generalized linear models. which is cumulative logit model in the first stage and the sequential logit model in second stage.Strong consistency of the maximum likelihood estimator in generalized linear models which has certain theory value and practical significance,it is used for the data analysis of the actual problem.In order to make reasonably analysis and further research. This paper mainly studies strong consistency of the maximum likelihood estimator in two stage models of generalized linear models. we mainly introduced the model structures,and how to model. We prove strong consistency of the maximum likelihood estimator in two stage models under certain conditions. This article provides some theoretical basis for the future application. This article consists of four chapters, mainly content is as follows.The first chapter mainly introduces the research background and the basic concepts of the generalized linear models.The Second chapter build the two stage models, which is cumulative Logit model in the first stage and sequential Logit model in the second stage.In the third chapter, we remove the restriction that{zi,i≥1}is bounded. Under the conditions‖zn‖=o(logn)andλminΣzizi> cna,we odtain consistency of the maximum likelihood estimator.