Mathematical Sciences: Some New Bootstrap Methods for SampleSurveys

在统计文献中，已经提出了许多用于抽样调查中的方差估计和可信区间的重抽样方法。在大多数情况下，它们的理论性质并不被很好地理解，并且几乎没有证据表明这些方法比基于线性化和正态近似的标准方法有显著的改进。拟议的研究涉及将最近关于通过分层随机抽样获得的数据的重抽样技术的基础工作扩展到更复杂的调查设计。特别是，这涉及到适用于双抽样和两阶段整群抽样计划的Edgeworth展开理论的发展。该提案的第二部分描述了抽样调查中基于非参数预测的推断方法，该方法利用现有的Bootstrap方法来估计条件分布。除了理论工作外，还将对所提出的方法进行彻底的数值研究，并展示对实际数据的应用。在今天的“信息时代”，收集的数据量越来越大，对可靠的数据汇总技术的需求从未像现在这样迫切。不幸的是，在实际问题中遇到的许多数据并不满足标准统计方法良好工作所必需的条件。大量的信息往往阻碍或至少阻碍了对这些潜在困难的识别，因此，盲目应用许多统计程序是司空见惯的。此外，还需要不断开发新的统计方法，用于分析日益复杂的抽样设计。拟议的研究是正在进行的努力的一部分，目的是开发广泛适用和“可靠”的统计方法来分析调查数据。拟议的方法将广泛使用速度更快的计算机，从而使几年前还不可行的统计技术得以常规使用。

Numerous resampling methods for variance estimation and confidence intervals in sample surveys have been proposed in the statistical literature. In most cases, their theoretical properties are not well understood and there is little evidence that the methods offer a significant improvement over standard approaches based on linearization and normal approximation. The proposed research involves extending recent foundational work on resampling techniques for data obtained by stratified random sampling to more complex survey designs. In particular, this involves the development of Edgeworth expansion theory appropriate for double sampling and two-stage cluster sampling plans. A second component of the proposal describes a nonparametric prediction-based approach to inference in sample surveys which utilizes existing bootstrap methods for estimating conditional distributions. In addition to theoretical work, a thorough numerical investigation of the proposed methods will be conducted and applications to real data will be presented. In today's "Information Age" an ever-increasing quantity of data is collected and the need for reliable data summary techniques has never been more critical. Unfortunately, much of the data encountered in practical problems does not satisfy the conditions necessary for standard statistical methods to work well. The sheer quantity of information often prohibits or, at least, inhibits the identification of these potential difficulties and hence blind application of many statistical procedures is commonplace. In addition, there is a constant need to develop new statistical methodology which can be used to analyze increasingly complex sampling designs. The proposed research is part of an ongoing effort to develop widely applicable and "robust" statistical methods for analyzing survey data. The proposed methods will utilize widespread access to faster computers allowing statistical techniques which were not feasible only a few years ago to be used routinely.