基于Stein损失污染数据情形下刻度参数的经验贝叶斯估计

Empirical Bayes Estimation of Scale Parameter Under Stein Loss with Contaminated Data

本文研究基于污染数据情形的一类广义指数分布刻度参数的经验贝叶斯估计问题.在stein损失函数下,导出刻度参数的贝叶斯估计以及利用解卷积的核方法构造了该参数的经验贝叶斯估计.在适当的条件下,基于超平滑误差分布类证明所提出的经验贝叶斯估计的渐近最优性.

This paper considers the empirical Bayes estimation problem for the scale parameter of a generalized exponential distribution（GED） with contaminated data. Under the stein loss, the Bayes estimator of the scale parameter is derived and the empirical Bayes（EB） estimator is constructed via a deconvolution kernel method. The asymptotic optimality of the proposed EB estimator is shown for the type of supersmooth errors distribution under suitable conditions.