Asymptotic Theory and Resampling Methods for High Dimensional Data

高维数据的渐近理论和重采样方法

• 批准号: 1310068
• 负责人: Soumendra Lahiri
• 金额: $ 20万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-07-01 至 2017-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1310068&HistoricalAwards=false
• 关键词: Asymptotic; Theory; Resampling; Methods; Dimensional

This project seeks to make important theoretical and methodological contributions to several critical areas of nonparametric statistical inference for high dimensional data. Specifically, this project concentrates on (i) developing empirical likelihood methods for high dimensional data that, among other applications, allows for simultaneous testing of a large number of hypotheses with user-specified confidence levels even with a moderate sample size; (ii) developing bootstrap methodology for high dimensional data for post-variable selection inference; (iii) developing limit theory for studying first- and higher- order asymptotic properties of statistical methods in high dimensions; and (iv) investigating theoretical properties of the proposed and existing resampling methods in high dimensions.In recent years, high dimensional data appear routinely in many areas of sciences (e.g., Molecular Genetics, Finance, Climate studies, brain mapping, etc.) and in an ever increasing number of everyday activities (e.g., social networking, internet browsing, etc.). This presents unique challenges for information extraction, as traditional statistical methods do not perform well in such "needle in a haystack" situations - where the relevant information is confounded by the presence of a huge number of irrelevant variables. The proposed research seeks to address this need directly by developing novel statistical methods for high dimensional data without stringent assumptions on the data structure.

该项目旨在为高维数据的非参数统计推断的几个关键领域做出重要的理论和方法贡献。具体而言，该项目集中于（i）开发高维数据的经验似然方法，该方法允许在中等样本量下同时测试具有用户指定置信水平的大量假设;（ii）开发用于后变量选择推断的高维数据的bootstrap方法;（iii）发展极限理论，以研究高维统计方法的一阶及高阶渐近性质;以及（iv）研究所提出的和现有的高维重传方法的理论性质。近年来，高维数据通常出现在许多科学领域（例如，分子遗传学、金融学、气候研究、脑图谱等）并且在越来越多的日常活动中（例如，社交网络、因特网浏览等）。这对信息提取提出了独特的挑战，因为传统的统计方法在这种“大海捞针”的情况下表现不佳-在这种情况下，相关信息被大量不相关变量的存在所混淆。所提出的研究旨在通过开发新的统计方法来直接满足这一需求，而无需对数据结构进行严格的假设。