Robust empirical Bayes small area estimation with density power divergence
Robust empirical Bayes small area estimation with density power divergence
复制标题
DOI：
10.1093/biomet/asz075
复制
发表时间：
2020-06-01
期刊：
影响因子：
2.7
通讯作者：
Sugasawa, S.
中科院分区：
文献类型：
--
作者：
Sugasawa, S.
被称为Fay-Herriot模型的两阶段正态分层模型和经验贝叶斯估计器被广泛用于获得小范围内的间接和基于模型的均值估计。然而，当假设的正态分布不准确时，经验贝叶斯估计器的性能可能很差。本文提出了一种利用密度功率散度的简单修正方法，并提出了一种新的鲁棒经验贝叶斯小面积估计器。根据模型参数鲁棒估计量的渐近性质，推导了该估计量的均方误差和估计均方误差。通过仿真和实测数据的应用，研究了该方法的数值性能。
A two-stage normal hierarchical model called the Fay-Herriot model and the empirical Bayes estimator are widely used to obtain indirect and model-based estimates of means in small areas. However, the performance of the empirical Bayes estimator can be poor when the assumed normal distribution is misspecified. This article presents a simple modification that makes use of density power divergence and proposes a new robust empirical Bayes small area estimator. The mean squared error and estimated mean squared error of the proposed estimator are derived based on the asymptotic properties of the robust estimator of the model parameters. We investigate the numerical performance of the proposed method through simulations and an application to survey data.