基于γ散度的稳健小域估计方法

Robust Small Area Estimation Method Based on γ-Divergence

摘要: 被称为Fay-Herriot模型的两阶段正态分层模型被广泛应用于获得小范围内基于模型的均值估计。但是，当数据中出现异常值时，经验贝叶斯估计方法的性能可能很差，估计量会受到异常值的过度影响。本文提出了一种利用密度幂散度的修正方法，并提出了一种新的稳健经验贝叶斯小域估计方法，该方法对存在异常值的数据进行估计时有不错的效果。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并估计均方误差。通过数值模拟与实证分析，研究了该方法的数值性能，相比于其他估计量在处理异常值方面表现更为稳健。

Abstract: The two-stage normal hierarchical model known as the Fay-Herriot model is widely used to obtain model-based mean estimates for small areas. However, when outliers are present in the data, the performance of empirical Bayes estimation methods may be poor, and the estimators can be excessively influenced by outliers. This paper proposes a modification method utilizing density power divergence and introduces a new robust empirical Bayes small area estimation method, which performs well when estimating data with outliers. Based on the asymptotic properties of the robust estimator of model parameters, the mean squared error (MSE) of this estimator is derived and estimated. Through numerical simulations and empirical analyses, the numerical performance of this method is studied, demonstrating its robustness in handling outliers compared to other estimators.