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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2023, Vol. 40 ›› Issue (1): 69-82.doi: 10.3969/j.issn.1005-3085.2023.01.005

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分层先验总体中总体总量的经验贝叶斯预测

胡桂开,   周古辛,   肖新海,   桂洋明   

  1. 东华理工大学理学院，南昌 330013
  • 出版日期:2023-02-15 发布日期:2023-04-11
  • 基金资助:
    国家自然科学基金 (11661003)；江西省自然科学基金 (20192BAB201006).

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

HU Guikai,   ZHOU Guxin,   XIAO Xinhai,   GUI Yangming   

  1. School of Science, East China University of Technology, Nanchang 330013
  • Online:2023-02-15 Published:2023-04-11
  • Supported by:
    The National Natural Science Foundation of China (11661003); the Natural Science Foundation of Jiangxi Province (20192BAB201006).

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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。

关键词: 经验贝叶斯预测, 总体总量, 预测均方误差, 有限总体

Abstract:

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.

Key words: empirical Bayes prediction, population total, prediction mean squared error, finite population

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