广义估计方程的渐近理论-概率率与数理统计专业论文.docxVIP

II II THE ASYMPTOTIC THEORY FOR GENERALIZED ESTIMATING EQUATIONS ABSTRACT The methods of generalized estimating equations are a class of important way to study longitudinal data，which are the extensions of generalized linear models．Longitudinal data are a class of important data frequently encountered and dealed with in survival analysis，econometrics and insurance financial．In the longitudinal data，observation data of the same individual for many times are relevant but its correlation matrix is unknown, while the observations of differ- ent individual are independent．It is based on the asymptotic properties of re- gression parameter that the methods of generalized estimating equations is used in statistical analysis． This paper mainly study the asymptotic properties of roots of generalized estimating equations．Firstly，an interpretation of the symbols used in this paper is given, as well as an introduction to the generalized estimating equations．At the same time，gives some conditions on the show of the asymptotic properties of generalized estimating equations．Secondly，the paper proves the main pa- rameter’s asymptotic existence and consistency of estimating sequence under the conditions that the response variables are one-dimensional and general link functions．Finally，the paper proves asymptotic normality of estimating sequence under conditions that the response variables are one-dimensional and general PAGE PAGE IV link functions and residuals are martingale difference sequence．The paper generalizes the asymptotic results of Xie and Yang(Ann．Statist．31(2003)： 310-347)and Balan and Schiopu-Kratina ( Ann. Statist. 33(2005)：522-540)． KEY WORDS：generalized estimating equations；link functions；asymptotic existence；consistency；asymptotic normality 目 录 第 1 章 绪论 1 1.1 选题的意义 1 1.2 研究背景 1 1.3 本文主要工作及创新之处 3 第 2 章 广义估计方程简介 4 2.1 预备知识 4 2.2 广义估计方程简介 5 2.3 本章小结 9 第 3 章 广义估计方程估计的渐近存在性和相合性 10 3.1 定理及相关引理 10 3.2 估计的渐近存在性和相合性的证明