分层先验总体中总体总量的经验贝叶斯预测  

Empirical Bayes Prediction of Population Total in a Finite Population with Hierarchical Priors

作　　者：胡桂开 周古辛 肖新海 桂洋明 HU Guikai;ZHOU Guxin;XIAO Xinhai;GUI Yangming(School of Science,East China University of Technology,Nanchang)

机构地区：[1]东华理工大学理学院,南昌330013

出　　处：《工程数学学报》2023年第1期69-82,共14页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11661003);江西省自然科学基金(20192BAB201006)。

摘　　要：对具有分层逆伽马先验总体中总体总量的经验贝叶斯预测进行研究。首先,提出一种新方法得到总体总量的贝叶斯预测,并在此基础上获得总体总量的经验贝叶斯预测。其次,分情形探讨了经验贝叶斯预测的性质,结果表明它是渐近最优的,并在预测均方误差意义下优于最佳线性无偏预测。最后,通过模拟研究论证了论文的主要结论。The empirical Bayes prediction of population total in a finite population with normal inverse-Gamma priors is investigated.Firstly,the Bayes prediction for population total is obtained by a new method.On the basis,the empirical Bayes predictions are proposed.Secondly,the performances of empirical Bayes prediction are analyzed by two cases.The result showed that empirical Bayes prediction is asymptotically optimal and can be proved to be the best linear unbiased prediction under the prediction mean squared error.Finally,a simulation study is used to illustrate the proposed results.

关 键 词：经验贝叶斯预测 总体总量 预测均方误差 有限总体 

分 类 号：O212.4[理学—概率论与数理统计]