Some Properties for the Estimators in Linear Mixed Models  

作　　者：Zai-xing Li Yan Cui Wang-li Xu 

机构地区：[1]College of Science, China University of Mining and Technology (Beijing) [2]School of Statistics, Renmin University of China

出　　处：《Acta Mathematicae Applicatae Sinica》2013年第1期105-116,共12页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China (No. 11001267);the Fundamental Research Funds for the Central Universities in China (No. 2009QS02);Supported by the National Natural Science Foundation of China (No. 10701079, 10871001)

摘　　要：Linear mixed models （LMMs） have become an important statistical method for analyzing cluster or longitudinal data. In most cases, it is assumed that the distributions of the random effects and the errors are normal. This paper removes this restrictions and replace them by the moment conditions. We show that the least square estimators of fixed effects are consistent and asymptotically normal in general LMMs. A closed-form estimator of the covariance matrix for the random effect is constructed and its consistent is shown. Based on this, the consistent estimate for the error variance is also obtained. A simulation study and a real data analysis show that the procedure is effective.Linear mixed models （LMMs） have become an important statistical method for analyzing cluster or longitudinal data. In most cases, it is assumed that the distributions of the random effects and the errors are normal. This paper removes this restrictions and replace them by the moment conditions. We show that the least square estimators of fixed effects are consistent and asymptotically normal in general LMMs. A closed-form estimator of the covariance matrix for the random effect is constructed and its consistent is shown. Based on this, the consistent estimate for the error variance is also obtained. A simulation study and a real data analysis show that the procedure is effective.

关 键 词：Moment conditions LMMs CONSISTENCY Asymptotical normality 

分 类 号：O212.1[理学—概率论与数理统计] TN911.73[理学—数学]