AI 中文总结
研究针对异方差总体分层抽样，开发贝叶斯最优样本分配方法，解决现有理论需已知设计参数的问题，通过在特定模型下优化设计并与其他方法比较，发现所提方法性能良好，还应用于分析公共慈善机构收入。
AI 中文摘要
我们为异方差总体中的分层抽样开发了一种贝叶斯最优样本分配方法。现有最优分配理论通常假定已知某些可能未知的设计参数，导致从业者在规划样本时用基于调查的估计值替代，且常未考虑这种替代对样本效率的影响。贝叶斯决策理论可避免此类替代并应用于样本分配。20世纪60年代中期到80年代初对贝叶斯样本优化方法研究较多，但此后被忽视。早期工作的一个局限是未考虑异方差误差结构。本文在具有异方差误差的单变量回归模型下优化设计，解决了早期工作的局限，同时阐述了贝叶斯设计方法。我们确定了模型下的最优贝叶斯分配，然后在多种设置下将其与基于设计和模型辅助的关键替代方法的性能进行比较，发现所提方法在考虑的场景中表现良好或更优。我们应用这些方法分析公共慈善机构的收入，使用公开可用的美国国税局990表格数据。
英文摘要
We develop a Bayesian optimal sample allocation approach for stratified sampling in heteroscedastic populations. Existing optimal allocation theory typically assumes knowledge of certain design parameters (e.g., strata variances) that may be unknown, leading practitioners to substitute in survey-based estimates when planning samples, often without considering the effects of this substitution on sample efficiency. Bayesian decision theory for optimal experimental design avoids such substitutions and can be applied to sample allocation. Bayesian sample optimization methods were studied heavily from the mid-1960s through early 1980s, but have been overlooked since, in spite of modern computing advances that have facilitated a proliferation of Bayesian methods in other areas of statistics. A limitation of this early Bayesian sample design work is that it did not accommodate heteroscedastic error structures, which underlie commonly used ratio estimation models. Our paper, which optimizes the design under a univariate regression model with heteroscedastic errors, addresses this limitation of earlier work, while illustrating the Bayesian approach to design. We identify the optimal Bayesian allocation under our model, then compare performance of the proposed Bayesian sampling strategy with that of key design-based and model-assisted alternatives across several settings, finding that the proposed methods do as well or better than the alternatives under the scenarios considered. We apply our methods in analyzing revenues of public charities, using publicly available IRS Form 990 data.
Comments52 pages, 5 figures, 15 tables
