Asymptotic Normality Of Logistic Additive Partial Linear Model

Generalized additive partial linear model is derived from generalized linear model.On the basis of generalized linear model,the nonlinear part can be added,which makes the generalized additive partial linear model possess the advantages of the nonparametric model and the parametric model simultaneously.Generalized additive partial linear model has the capability to deal with discrete data,such as count data and attribute data,and can also improve the utilization of the data information by nonparametric part and then makes the forecast more accurate in practical application.Generalized additive partial linear model also has a corresponding generalized estimation equation when dealing with longitudinal data.Longitudinal data often appears in economics,sociology and medical research and so on.With the advent of the era of big data,the structure of longitudinal data has become more complex and the dimension increase correspondingly,even high-dimensional,which cause the so-called "dimension of the curse".In the normal regression model,the study is usually carried out under the condition that the sample size tends to be infinite and the covariate dimension is fixed.Therefore,the study of the longitudinal data with divergent dimension has a certain academic value.In this paper,we use Logistic additive partial linear model and assume that the simple size is toward infinity and the dimension of covariate is diverging.Under these conditions we study the asymptotic existence,consistency and asymptotic normality of the generalized estimating equation.The means we used in this paper include topological homeomorphic theorem,spline function,Lyapunov theorem and median theorem.The corresponding results in the literature have been improved.