Asymptotic Normality Of The Two-Stage Cumulative Logistic Model

The General Linear Model is the direct extension of the General Linear Regression Model, in which the distributions of responses comply with the exponential family distributions. There are many applications of statistical models belonging to the General Linear Model. The responses of Logistic model are categorical variables, in case the categories of the observation data are more than two. Through the data classification, the model is extended to multiple classification variable models. The cumulative logistic regression model as a multivariate statistical method, commonly be used in processing the classification attribute data.This thesis gives two-stage cumulative logistic regression model as following:The state of each category has similar properties, while different types of state property are not similar. Model is divided into two steps:The first step, if the data have k states, which are divided into t categories, we observe which category the object belongs to. The second step, we determine the state of the data in the j th category. Fahrmeir and Kaufinann assumed that‖xn‖=o(logn) and the smallest eigenvalue of (?)(1xi’) is greater than cna(constant c>0, α>0), where xi is a covariant vector, to prove the asymptotic normality of cumulative logistic model. Under the same conditions, we study the two-stage cumulative logistic model, when n is large enough, there exists a maximum likelihood estimator βn of the true regression parameter β0, such that the likelihood equation holds in probability which tends to1, and βn converges to β0in probability, we can prove that βn has properties of weak consistency and asymptotic normality.