Collaborative Research: Small-Area Estimation - A Growing Problem for the Next Millennium

大规模抽样调查通常是为了对大地理区域的各种感兴趣的特征作出可靠的估计。然而，为了有效规划保健、社会和其他服务，越来越需要对较小的地理区域和亚人口，即通常所说的小地区（或小域）作出类似的估计。当数据用于在不同群体之间分配政府资金时，小地区统计的准确性尤为重要。该项目侧重于开发新的鲁棒小区域估计方法和相关的模型诊断。估计方法将在一般的多层次模型下发展，这将有助于解决各种小面积估计问题。为了解决与多层次模型相关的模型验证和模型选择的一个重要但很大程度上被忽视的方面，提出了一个使用样本分裂技术的测试。将样本分成估计集和验证集也可用于评估模型的实际功率。随着社会科学家发现需要使用复杂的多层次模型来解决他们的问题，这一研究领域将继续发展。这项研究是调查人员在各种联邦、州和私人机构遇到的小区域估计问题的经验的产物。重要的是，这个项目将解决一个关键的实际问题，这个问题是全世界许多政府和私人机构工作的基础。此外，对小面积估计的研究也将对调查抽样、广义线性混合模型、经验最佳预测理论、线性经验贝叶斯、方差分量估计、重采样方法、模型诊断、高阶渐近和统计计算等方面的文献做出重要贡献。由于不同类型的研究人员（如调查抽样人员、主流统计学家、社会科学家）的兴趣，在我们进入下一个千年时，小区域估计仍将是调查抽样中最有趣的问题之一。

Large scale sample surveys are usually designed to produce reliable estimates of various characteristics of interest for large geographic areas. However, for effective planning of health, social, and other services, there is a growing demand to produce similar estimates for smaller geographic areas and subpopulations, commonly referred to as small-areas (or small-domains). The accuracy of small-area statistics is especially crucial when data are used to apportion government funds among various groups.This project focuses on development of new robust small-area estimation methods and the associated model diagnostics. The estimation methods will be developed under general multi-level models which will be useful in solving a variety of small-area estimation problems. To address an important and yet largely neglected aspect of model validation and model selection associated with multi-level models, a test using a sample splitting technique is proposed. Splitting the sample into an estimation set and a validation set can also be used for assessing the actual power of the model. This area of research will continue to grow as social scientists find the need to use complex multi-level models to solve their problems.The research is an outgrowth of the investigators' experiences with small-area estimation problems encountered by various federal, state, and private agencies. Importantly, this project will address a crucial practical problem underlying the work of many governmental and private institutions throughout the world. Further, this research on small-area estimation also will contribute significantly to the literature on survey sampling, generalized linear mixed models, empirical best prediction theory, linear empirical Bayes, variance component estimation, resampling methods, model diagnostics, higher order asymptotics, and statistical computing. Because of the interests of different types of researchers (e.g., survey samplers, main stream statisticians, social scientists), small-area estimation will remain one of the most intriguing problems in survey sampling as we advance into the next millennium.