Mathematical Sciences: Some New Bootstrap Methods for SampleSurveys

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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.