Optimal Credibility Estimation of Random Parameters in Hierarchical Random Effect Linear Model  

作　　者：WEN Limin FANG Jing MEI Guoping WU Xianyi 

机构地区：[1]School of Mathematics and Information Science, Jiangxi Normal University [2]School of Information Management, Jiangxi University of Finance and Economics [3]Department of Statistics and Actuarial Science, East China Normal University

出　　处：《Journal of Systems Engineering and Electronics》2015年第5期1058-1069,共12页系统工程与电子技术（英文版）

基　　金：supported by the National Science Foundation of China under Grant Nos.71361015,71340010,71371074;the Jiangxi Provincial Natural Science Foundation under Grant No.20142BAB201013;China Postdoctoral Science Foundation under Grant No.2013M540534;China Postdoctoral Fund special Project under Grant No.2014T70615;Jiangxi Postdoctoral Science Foundation under Grant No.2013KY53

摘　　要：In the hierarchical random effect linear model, the Bayes estimator of random parameter are not only dependent on specific prior distribution but also it is difficult to calculate in most cases. This paper derives the distributed-free optimal linear estimator of random parameters in the model by means of the credibility theory method. The estimators the authors derive can be applied in more extensive practical scenarios since they are only dependent on the first two moments of prior parameter rather than on specific prior distribution. Finally, the results are compared with some classical models and a numerical example is given to show the effectiveness of the estimators.In the hierarchical random effect linear model, the Bayes estimator of random parameter are not only dependent on specific prior distribution but also it is difficult to calculate in most cases. This paper derives the distributed-free optimal linear estimator of random parameters in the model by means of the credibility theory method. The estimators the authors derive can be applied in more extensive practical scenarios since they are only dependent on the first two moments of prior parameter rather than on specific prior distribution. Finally, the results are compared with some classical models and a numerical example is given to show the effectiveness of the estimators.

关 键 词：Bayes theory credibility estimator hierarchical linear model random effect 

分 类 号：O212[理学—概率论与数理统计] TP391.12[理学—数学]