Empirical Best Prediction of Small Area Means Based on a Unit-Level Gamma-Poisson Model

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Emily J. Berg
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引用次数: 0

Abstract

Existing small area estimation procedures for count data have important limitations. For instance, an M-quantile-based method is known to be less efficient than model-based procedures if the assumptions of the model hold. Also, frequentist inference procedures for Poisson generalized linear mixed models can be computationally intensive or require approximations. Furthermore, area-level models are incapable of incorporating unit-level covariates. We overcome these limitations by developing a small area estimation procedure for a unit-level gamma-Poisson model. The conjugate form of the model permits computationally simple estimation and prediction procedures. We obtain a closed-form expression for the empirical best predictor of the mean as well as a closed-form mean square error estimator. We validate the procedure through simulations. We illustrate the proposed method using a subset of data from the Iowa Seat-Belt Use survey.
基于单位水平Gamma-Pisson模型的小区域均值经验最佳预测
现有的计数数据的小面积估计程序具有重要的局限性。例如,如果模型的假设成立,则已知基于M-量的方法不如基于模型的过程有效。此外,泊松广义线性混合模型的频率论推理过程可能是计算密集型的,或者需要近似。此外,区域级别的模型不能包含单位级别的协变量。我们通过开发单位水平伽玛-泊松模型的小面积估计程序来克服这些限制。该模型的共轭形式允许计算上简单的估计和预测过程。我们得到了均值的经验最佳预测器的闭合形式表达式以及闭合形式的均方误差估计器。我们通过仿真验证了该过程。我们使用爱荷华州安全带使用调查的数据子集来说明所提出的方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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