Some Contributions to Sampling Theory with Applications

本项目将开发小面积估算方法。小面积估计通常需要使用模型，无论是显式的还是隐式的。这些基于模型的估计可能与直接估计有很大的不同，特别是对于样本量非常小的地区。虽然基于模型的小面积估计非常有用，但这些估计的一个潜在困难是，当汇总时，对较大地理区域的总体估计可能与通常被认为更可靠的相应直接估计有很大不同。避免这个问题的一种方法是所谓的“基准方法”，它相当于修改这些基于模型的估计，以便在更大的地理区域获得相同的总估计。本研究项目将使用单一模型开发一个通用的两阶段贝叶斯基准测试程序。例如，使用这种方法，州人均收入估计将以全国人均收入估计为基准，相应的县估计将以基准国家估计为基准，而不需要两个单独的模型。研究人员将发展贝叶斯伪经验似然估计有限的人口分布函数和相应的人口分位数。这种方法将扩展到在小区域范围内估计人口分布函数，在这种情况下，目标是相同的，但需要对局部区域进行个别估计，通常涉及非常小的样本量。这使得有必要通过连接基于从人口普查或其他行政记录中获得的辅助信息的模型来“借力”。研究的第三部分是基于copula模型的信息抽样推理。在本项目中考虑的联结模型允许根据观察结果对选择概率进行依赖性建模。这与当前可用的方法相反，后者在此建模中假定独立性。从这个项目中开发的方法有多种应用，将对广泛的调查研究人员有价值。特别是，关于两阶段基准的研究将与许多联邦统计机构有关。关于经验可能性的工作，特别强调对小地区贫困指标的估计，是一个非常及时的课题。最后，信息性抽样的研究将对包括流行病学和经济学在内的许多领域的研究人员有价值。

This project will develop methods for small area estimation. Small area estimation generally requires the use of models, either explicitly or implicitly. These model-based estimates can differ widely from the direct estimates, especially for areas with very low sample sizes. While model-based small area estimates are very useful, one potential difficulty with these estimates is that when aggregated, the overall estimate for a larger geographical area may be quite different from the corresponding direct estimate, which is usually believed to be more reliable. One way to avoid this problem is the so-called "benchmarking approach," which amounts to modifying these model-based estimates so that one gets the same aggregate estimate for the larger geographical area. This research project will develop a general two-stage Bayesian benchmarking procedure using a single model. With this approach, for example, the state per capita income estimates would be benchmarked to the national per capita income estimate and the corresponding county estimates to the benchmarked state estimates without requiring two separate models. The researcher will develop Bayesian pseudo-empirical likelihood for estimating finite population distribution functions and the corresponding population quantiles. The approach will be extended to estimation of the population distribution function in the small area context where the goal is the same but for which one needs individual estimates for local areas, often involving very small sample sizes. This makes it necessary to "borrow strength" through linking models based on auxiliary information available from censuses or other administrative records. The third component of the research involves inference under informative sampling based on copula models. The copula model to be considered in this project allows dependence in modeling the selection probabilities in terms of the observed outcomes. This is in contrast to the currently available method, which assumes independence in this modeling.The methods to be developed from this project have multiple applications and will be of value to a broad range of survey researchers. In particular, the research on two-stage benchmarks will be of relevance for many of the Federal statistical agencies. The work on empirical likelihood, with particular emphasis on estimation of small area poverty indicators, is an extremely timely topic. Finally, the research on informative sampling will be of value to researchers across many fields, including epidemiology and economics.