Generalized estimating equation estimators with longitudinal data

Generalized estimating equations method as a powerful method for estimating parameters, is wildly used in many fields, such as biostatistics, econometrics and medical insurance, and so on. For longitudinal data, We should take account into within-subject correlation structure in order to improve efficiency of a estimator. It is often useful to suppose that there is a parametric assumption within-subject correlation in longitudinal data analysis. But unreasonable assumptions made on within-subject correlation structure can result in inefficient estimation for parameters or even result in misspecification. For the generalized estimating equations with longitudinal data, we propose the extended GMM methods and extended EL methods and construct the large sample properties for our estimators. One of the proposed EL methods which is called block empirical likelihood is robust because of avoiding any assumptions on withinsubject correlation structure. We also provide two simulation examples to illustrate the finite properties for our estimators.