Asymptotic Properties Of Compound Order Logit Model With Diverging Number Of Covariates

The generalized estimating equations(GEE)is an important tool for analyzing longitudinal data.It can be used to estimate the regression coefficients of multiple models such as marginal model,random effect model and transfer model and solves the statistical problems caused by the data correlation or the abnormal distribution of dependent variable.In short,it broadens the idea of longitudinal data analysis.In this thesis,we mainly study the asymptotic properties of the generalized estimation equation of the compound order model with diverging number of covariates.The dependent variables studied in this thesis are attribute variables,and the number of attributes is greater than two.First,based on the multidimensional generalized linear model,a generalized estimation equation of the compound order model is established.Then,the existence and consistency theorems of its parameter estimation are given in the case of the diverging number of covariates.And we prove it with the fixed point theorem and the existence theorem of the root of the multivariate nonlinear system.The lemmas and the proof process are more universal than Wang(2011).At the same time,the consistency theorem also shows the feasibility of the model.Finally,we introduce the asymptotic normality theorem and relevant lemmas of generalized estimation equation and prove the validity of the theorem by Linder-feller condition,central limit theorem,etc.Asymptotic normality provides the basis for parameter estimation.In this thesis,we mainly analyze the large sample asymptotic theory of GEE estimation of the compound order model and provide a new method for the longitudinal data analysis of multiatribute dependent variables.