Organization of Small Area Estimators Using a Generalized Linear Regression Framework
Organization of Small Area Estimators Using a Generalized Linear Regression Framework
复制标题
使用广义线性回归框架组织小面积估计器
DOI：
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发表时间：
1999
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通讯作者：
D. Marker
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文献类型：
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作者：
D. Marker
在过去的25年里，从抽样调查中得出小地区或领域（整个人口的子集）估计数的特殊问题在调查抽样文献中受到越来越多的关注。许多尝试得到这样的估计已经要么特设的方法为speci®c问题，假设speci®c模型的数据，或尝试应用大样本抽样理论的问题，小样本。在这篇文章中，现有的小面积估计，包括贝叶斯已经提出。目的是对问题和进行这种估计的方法有更一致的了解。典型的调查抽样估计方法是设计调查以产生设计一致的估计，即估计其对所有可能样本的期望对于未知参数是一致的。基什（1987）指出，并非所有需要估计的领域都是"主要领域“，也就是说，可以产生可接受精度的基于设计的估计的总体领域。经常需要对较小的"次要领域“进行估计，但标准的基于设计的估计太不稳定。感兴趣的次要领域取决于主题。在许多人口和健康调查中，感兴趣的次要领域包括地理和种族的组合，在这篇文章中，现有的小面积估计，包括贝叶斯的，已经提出。Ghosh和Rao（1994）对当前文献中的许多技术进行了出色的描述，指出了开发模型时聚合水平的重要性。在这篇文章中，文献进行了审查的估计。然后从一般线性回归的角度组织估计量，总结并显示某些方法可以被视为其他方法的微小变化或概括。这包括推导条件，在此条件下，可以将综合估计视为一种回归形式。本文的目标是将用于小区域估计的各种方法汇总在一起。从这一审查更清楚地了解目前的技术和它们之间的相互关系是显而易见的。
For the last 25 years the special problems of deriving estimates for small areas or domains (subsets of the entire population) from sample surveys have received increasing attention within the survey sampling literature. Many attempts to derive such estimators have been either ad hoc approaches for speci®c problems, assuming speci®c models for the data, or attempts to apply large-sample sampling theory to problems of small samples. In this article existing small area estimators are described, including Bayesian ones that have been proposed. The goal is to develop a more coherent understanding of the problem and methods with which such estimation can be undertaken. The typical survey sampling approach to estimation is to design the survey to produce design-consistent estimates, that is, estimates whose expectations over the set of all possible samples are consistent for the unknown parameters. Kish (1987) points out that not all domains for which estimates are desired are ``major domains,' that is, domains of the population for which design-based estimates of acceptable precision can be produced. Frequently estimates for smaller ``minor domains' are desired but the standard design-based estimates are too unstable. Minor domains of interest depend on the subject matter. In many demographic and health surveys, minor domains of interest include geography, and combinations of race, In this article existing small area estimators are described, including Bayesian ones that have been proposed. Ghosh and Rao (1994) provide an excellent description of many of the techniques found in the current literature, pointing out the importance of the level of aggregation at which the models are developed. In this article a literature review is conducted for the estimators. The estimators are then organized from a general linear regression perspective, summarizing and showing where certain methods can be viewed as minor variations or generalizations of others. This includes a derivation of the conditions under which it is possible to view synthetic estimation as a form of regression. The goal of this article is to pull together the wide range of approaches that have been used for small area estimation. From this review a clearer understanding of the present techniques and their interrelationships is apparent.