线性混合模型中一些估计的渐近性质.pdf

(Longitudinal Data) (Subject) (Mixed Model) b ǫ  Æ (MLE) (REML)  Æ (MLE) (REML) (LS) Æ Æ 3 Æ Æ ABSTRACT Longitudinal data has received much attention recently. There are a lot of examples of this data structure in many fields, such as biology, social science, eco- nomics and finance. Longitudinal data are often characterized by the dependence of repeated observations over time or space within the same subject. They are independent among different subjects, but dependent within the same subject. The linear mixed models have become an important statistical models for analyzing longitudinal data, in which the error could be used to describe the independent among subjects and the random effect could be used to describe the dependent among observations from one subject. And the parameter estimation is always one of the most popular directions in the research of mixed models with repeated measures. In most cases, it is assumed that the distributions of the random effects and the error are normal. However, it is not always the cases in practices. This thesis does not require the normal distribution of the random effect and error variablesand doesn’t base on MLE and REML methods which are used in most papers. We use the least square method and moment estimation method. We show that the least square estimators of fixed effects are jointly asymptotically normal in general linear mixed model, and the same conclusion for the variance estimator of error variables based on momen