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Bootstrap Methods in Modern Settings: Inference and Computation

现代环境中的引导方法：推理和计算

基本信息

批准号：
1915786
负责人：
Miles Lopes
金额：
$ 22万
依托单位：
University of California-Davis
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-07-01 至 2023-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1915786&HistoricalAwards=false
关键词：
Bootstrap Methods Modern Settings Inference

项目摘要

Bootstrap methods play a central role in statistical methodology, and are among the most widely used tools for uncertainty quantification. Although bootstrap methods have an extensive literature, their scope of applicability is far from being fully understood in modern statistical problems. This is especially the case when data are described by high-dimensional models with many unknown parameters, or when then the amount of data exceeds computational constraints. Motivated by these challenges, the proposed research has two main objectives, which are to (1) analyze the theoretical validity of bootstrap methods in high-dimensional models, and (2) develop novel ways of using bootstrap methods to enhance large-scale computations. The graduate student will focus on the analysis of bootstrap methods for high-dimensional and large-scale data. With regard to the first objective, the research will focus on overcoming certain limitations of the non-parametric bootstrap, particularly in the context of high-dimensional principal components analysis. This will be pursued through a generalization of the parametric bootstrap that is tailored to the statistics of interest. Examples of such statistics include those arising from the eigenvalues of sample covariance matrices. For the second objective, the research will explore bootstrap methods as a systematic way to estimate the errors of randomized algorithms. Given that bootstrap methods have been historically labeled as computationally intensive, this application is based on a relatively distinct perspective, since it seeks to use bootstrap methods to assist computation. In particular, bootstrap methods will be developed to obtain numerical error estimates that offer a practical alternative to worst-case error analysis.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

自举法在统计方法学中起着核心作用，是最广泛使用的不确定性量化工具之一。虽然自举法有广泛的文献，但在现代统计问题中，其适用范围还远远没有被完全理解。当数据由具有许多未知参数的高维模型描述时，或者当数据量超出计算限制时，尤其如此。在这些挑战的激励下，本研究有两个主要目标，即：(1)分析自举方法在高维模型中的理论有效性；(2)开发利用自举方法增强大规模计算的新方法。研究生将专注于分析高维和大规模数据的自举方法。关于第一个目标，研究将侧重于克服非参数自举的某些局限性，特别是在高维主成分分析的背景下。这将通过根据感兴趣的统计数据定制的参数自举的泛化来实现。这种统计的例子包括由样本协方差矩阵的特征值产生的统计。对于第二个目标，研究将探索bootstrap方法作为一种系统的方法来估计随机算法的误差。考虑到引导方法在历史上被标记为计算密集型，这个应用程序基于一个相对不同的角度，因为它试图使用引导方法来辅助计算。特别是，将开发自举方法来获得数值误差估计，为最坏情况误差分析提供实用的替代方案。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。