纵向数据下广义估计方程估计

Generalized Estimating Equation Estimators with Longitudinal Data

广义估计方程方法是一种最一般的参数估计方法,广泛地应用于生物统计、经济计量、医疗保险等领域.在纵向数据下,由于组间数据是相关的,为了提高估计的效率,广义估计方程方法一般需要考虑个体组内相关性.因此,大多数文献对个体组内的协方差矩阵进行参数假设,但假设的合理性及协方差矩阵估计的好坏对参数估计效率产生很大影响,同时参数假设也可能导致模型误判.针对纵向数据下广义估计方程,本文提出了改进的GMM方法和经验似然方法,并对给出的估计量建立了大样本性质.其中分块的思想,避免了对个体组内相关性结构进行假设,从这种意义上说,这种方法具有一定的稳健性.我们还通过两个模拟的例子,考察了文中提出估计量的有限样本性质.

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 within-subject correlation structure.We also provide two simulation examples to illustrate the finite properties for our estimators.