Asymptotic Normality Of The Sequential-Cumulative Logistic Two-Stage Model

Since the emergence of generalized linear model, at the time of the past century, scholars at home and abroad have done a lot of research and achieved a lot of fruitful results. With the development of science and technology, there are still many unknown results waiting for us to explore. Combined with previous studies, we mainly focused on discussion asymptotic properties of maximum likelihood estimation of generalized linear models. In order to study from the potential relationship between the regressors Xi and the responses Y, when calculating the probability of Y in the role of Xi, we can use many of the specific models.The most well-known model is the logistic model, there are also some common models, such as probit model and poisson model, and so on. On the basis of the sort of the sample data, this paper extends the general model to the two-stage model, which is formed with sequential model and cumulative model.At first this paper reviews the knowledge of the generalized linear models and the maximum likelihood estimation, and then describes the process of the formation of the two-stage model and defines the corresponding link function. Finally, under some mild conditions such as‖zn‖=o(logn) and the minimum eigenvalue of (?)zizi’s greater than cnα for some c>0,α>0,we establish the asymptotic normality of the maximum likelihood estimates of the two-stage model.