幂幂损失下正约束参数的贝叶斯估计量及其应用  

The Bayes Estimator of the Positive Restricted Parameter under the Power-Power Loss with an Application

作　　者：张应应 荣腾中[1,2] 李曼曼 ZHANG Yingying;RONG Tengzhong;LI Manman(Department of Statistics and Actuarial Science,Chongqing University,Chongqing,401331,China;Chongqing Key Laboratory of Analytic Mathematics and Applications,Chongqing University,Chongqing,401331,China)

机构地区：[1]重庆大学统计与精算学系,重庆401331 [2]重庆大学分析数学与应用重庆市重点实验室,重庆401331

出　　处：《应用概率统计》2023年第2期159-177,共19页Chinese Journal of Applied Probability and Statistics

基　　金：supported by the MOE Project of Humanities and Social Sciences on the West and the Border Area (Grant No. 20XJC910001);the National Social Science Fund of China (Grant No. 21XTJ001);the National Natural Science Foundation of China (Grant No. 12001068)。

摘　　要：所提出的幂幂损失函数对参数过大或过小具有均衡收敛速度或惩罚,具有本文列出的所有七个性质,因此建议用于正限制参数空间.然后在幂幂损失函数下计算参数的贝叶斯估计量、后验风险、综合风险和贝叶斯风险.接着,我们在一个分层正态–正态逆伽玛模型下解析地计算了这些量.最后,数值模拟验证了我们的理论研究.The proposed power-power loss function which has balanced convergence rates or penalties for its argument too large and too small,has all the seven properties listed in this paper,and thus it is recommended to use for the positive restricted parameter space.We then calculate the Bayes estimator,the posterior risk,the integrated risk,and the Bayes risk of the parameter under the power-power loss function.After that,we analytically calculate these quantities under a hierarchical normal and normal-inverse-gamma model.Finally,the numerical simulations exem-plify our theoretical studies.

关 键 词：贝叶斯估计量 正约束参数空间 幂幂损失函数 后验期望损失 分层正态–正态逆伽玛模型 

分 类 号：O212[理学—概率论与数理统计]