Mathematical Sciences: Some New Bootstrap Methods for SampleSurveys

统计文献中已经提出了许多样本调查中方差估计和置信区间的重抽样方法。在大多数情况下，它们的理论性质没有得到很好的理解，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提供了显著的改进。拟议的研究涉及将分层随机抽样获得的数据的重新抽样技术的最新基础工作扩展到更复杂的调查设计。特别地，这涉及到适用于双重抽样和两阶段群集抽样计划的Edgeworth展开理论的发展。该提案的第二部分描述了一种基于非参数预测的样本调查推理方法，该方法利用现有的自举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，并将其应用于实际数据。在今天的“信息时代”，收集的数据数量不断增加，对可靠的数据摘要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有效工作所必需的条件。大量的资料常常妨碍或至少妨碍查明这些潜在的困难，因此盲目应用许多统计程序是司空见惯的。此外，不断需要发展新的统计方法，用于分析日益复杂的抽样设计。拟议的研究是一项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。所提议的方法将利用更快速的计算机的广泛使用，使仅仅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.