Bayesian estimators for small area models shrinking both means and variances
Bayesian estimators for small area models shrinking both means and variances
复制标题
小区域模型的贝叶斯估计量缩小了均值和方差
DOI：
10.1111/sjos.12246
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发表时间：
2017
影响因子：
1
通讯作者：
T.
中科院分区：
文献类型：
--
作者：
Sugasawa;S.;Tamae;H. and Kubokawa;T.
对于区域水平数据的小区域估计，Fay-Herriot模型作为一种基于模型的方法被广泛使用。在Fay-Herriot模型中，通常假设抽样方差是已知的，而实际中使用的是抽样方差的估计量。因此，已知抽样方差的设置是不现实的，因此提出了几种方法来克服这一问题。在本文中，我们假设样本方差的直接估计量和样本均值都是可用的。利用这些信息，我们提出了一种贝叶斯但客观的方法，在Fay-Herriot模型中产生均值和方差的收缩估计。我们考虑了抽样方差的层次结构，并对模型参数设置了统一的先验，以保持模型的客观性。对于后验推断的有效性，我们证明了在温和的条件下，后验分布是适当的，并且具有有限的方差。我们通过模拟和实证研究来考察其数值性能。
For small area estimation of area‐level data, the Fay–Herriot model is extensively used as a model‐based method. In the Fay–Herriot model, it is conventionally assumed that the sampling variances are known, whereas estimators of sampling variances are used in practice. Thus, the settings of knowing sampling variances are unrealistic, and several methods are proposed to overcome this problem. In this paper, we assume the situation where the direct estimators of the sampling variances are available as well as the sample means. Using this information, we propose a Bayesian yet objective method producing shrinkage estimation of both means and variances in the Fay–Herriot model. We consider the hierarchical structure for the sampling variances, and we set uniform prior on model parameters to keep objectivity of the proposed model. For validity of the posterior inference, we show under mild conditions that the posterior distribution is proper and has finite variances. We investigate the numerical performance through simulation and empirical studies.