The Asymptotic Theory For Generalized Estimating Equations

The methods of generalized estimating equations are a class of important way to study longitudinal data, which are the extension of generalized linear models. Longitudinal data is a class of important data which is frequently encountered and has to deal with, such as in survival analysis, econometrics, insurance financial. In the longitudinal data, observation data of the same individual for many times is relevant but its correlation matrix is un-known. Besides the Observation on different individual is independ-ent. Statistical analysis using the methods of generalized estimating equations is based on the asymptotic properties of regression parameter.This paper is mainly study on the root of generalized estimating equations’ asymptotic properties. Firstly, A interpretation is given to the symbols used in this paper, also an introduction is made to the generalized estimating equa-tions.At the same time, the paper gives some conditions on the process of the asymptotic properties of proving generalized estimating equations. Secondly, the paper proves the main parameter’s asymptotic existence and consistency of estimating sequence under the conditions of general link functions and one-dimensional response variable. Finally, the paper proves asymptotic normal-ity of estimating sequence under general link functions, one-dimensional re- sponse variable and residual being martingale difference sequence. Besides the paper generalizes Xie and Yang(Ann. Statist.31(2003):310-347), and also the Balan and Schiopu-Kratina’s (Ann. Statist.33(2005):522-540) asymptotic re-sults.