Asymptotic Theory and Resampling Methods for High Dimensional Data

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，该项目侧重于(i)开发高维数据的经验似然方法，在其他应用中，允许同时测试大量具有用户指定置信度的假设，即使是中等样本量；（ii）开发用于变量后选择推理的高维数据的自举方法；（三）发展了用于研究高维统计方法一阶和高阶渐近性质的极限理论；(4)研究高维重采样方法的理论性质。近年来，高维数据经常出现在许多科学领域（例如，分子遗传学，金融，气候研究，大脑绘图等）和越来越多的日常活动中（例如，社交网络，互联网浏览等）。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。拟议的研究旨在通过开发新的高维数据统计方法来直接解决这一需求，而不需要对数据结构进行严格的假设。

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.