污染数据情形下线性指数分布参数的经验贝叶斯估计（英文）  

Empirical Bayes Estimation for Linear Exponential Distribution with Contaminated Data

作　　者：陈家清[1] 王玉 刘次华[2] CHEN Jiaqing;WANG Yu;LIU Cihua(Department of Statistics,College of Science,Wuhan University of Technology,Wuhan 430070,China;College of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan 430074,China)

机构地区：[1]武汉理工大学理学院统计系,湖北武汉430070 [2]华中科技大学数学与统计学院,湖北武汉430074

出　　处：《应用数学》2018年第4期949-957,共9页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(81671633);the Fundamental Research Funds for the Central Universities(WUT:2017IB011)

摘　　要：本文研究污染数据情形下线性指数分布参数的经验贝叶斯估计问题.在平方损失函数下,导出参数的贝叶斯估计以及利用解卷积的核方法构造该参数的经验贝叶斯估计.在合适的条件下,得到基于超平滑误差分布类所提出的经验贝叶斯估计的一致收敛速度.This paper considers the empirical Bayes estimation problem for the parameter of linear exponential distribution（LED） with contaminated data（error in variables）.The Bayes estimator of the parameter is derived and the empirical Bayes（EB） estimator is constructed via a deconvolution kernel method by the square loss function. Under the suitable conditions, the uniform convergence rates are obtained over a class of prior distributions of the proposed EB estimators for the type of supersmooth errors distribution.

关 键 词：经验贝叶斯估计 污染数据 收敛速度 线性指数分布 

分 类 号：O212.1[理学—概率论与数理统计]