Statistical Analysis Of Generalized Linear Model With Diverging Number Of Covariates

Generalized linear models is an important extension of classical linear model, which was introduced by Nelder and Wedderburm (1972) and has an extensive appli-cation in practical statistical analysis.Wang(2011) discusses the method of analysis for binary data with diverging number of covariates by generalized equation method, and establishes the asymptotic theory of the unknown parameters, but the assumptions on information matrix and dimension of covariate are too strict. Firstly, for maximum likelihood estimator of the unknown parameters in Logistic models with diverging number of covariates, under the weaker assumptions on information matrix and dimension of covariates and some regular conditions, this paper first proves weak convergence and ratio of convergence , asymptotic normality of linear combination and discusses asymptotic distribution of linear constraint of the unknown parameters for Wald test; Furthermore, under similar assumptions on information matrix and dimension of covariates and some other reg-ular conditions, for the Generalized linear models with multi-dimensional responses and diverging number of covariates, this paper discussed the corresponding asymptot-ic properties of quasi-maximum likelihood estimator of unknown parameters; Finally, the results of this paper are illustrated by Monte Carlo simulations.This paper consists of four chapters. Chapter 1 discusses the background of re-search and gives out some basic knowledge which is used in this paper; Chapter 2 introduces the main results in this paper which includes the asymptotic properties of maximum likelihood estimator of unknown parameters for Logistic model and Gen-eralized linear models with general link function; Chapter 3 proves all the results in Chapter 2; Chapter 4 makes a conclude and prospect of this paper.