Leveraging Covariate and Structural Information for Efficient Large-Scale and High-Dimensional Inference

大数据的泛滥伴随着大量的问题，这些问题以假设检验的形式出现，这些问题需要有效的方法来进行大规模和高维的推理。这些有影响力的方法必须同时涉及对多个研究单位的统计分析。传统的同时推理程序通常假定不同单元的假设是可以互换的。然而，在许多科学应用中，关于信号模式的外部协变量和结构信息是可用的。有效和准确地利用这些辅助信息将导致统计能力的提高，以及研究结果的可解释性增强。这项研究的主旨是推进大规模和高维推理的统计方法和理论，特别是将潜在有用的外部协变量和结构信息整合到推理过程中。本研究旨在发展创新的方法和理论，以解决大规模和高维推理中的几个重要问题。在项目1中，PI将引入一个新的多重测试程序，当有大量外部协变量可用时，该程序可以自动选择相关协变量，以提高推理效率。在项目2中，PI将开发一个新的多测试框架，可以集成各种形式的结构信息。由于先验信息很少是完全准确的，因此将特别注重开发对错误指定/不完美的先验信息具有健壮性的程序。在项目3中，PI将提出新的程序，用于在具有辅助信息的高维回归中进行同时推理。统计工具将用于确定有技能的基金经理，评估气候领域重建的表现，并以综合方式分析基因组数据。开发的方法和计算机代码将公之于众。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The proliferation of big data is accompanied by a vast number of questions, in the form of hypothesis tests, which call for effective methods to conduct large-scale and high-dimensional inferences. These influential methods must involve statistical analysis on many study units simultaneously. Conventional simultaneous inference procedures often assume that hypotheses for different units are exchangeable. However, in many scientific applications, external covariate and structural information regarding the patterns of signals are available. Exploiting such side information efficiently and accurately will lead to improved statistical power, as well as enhanced interpretability of research results. The main thrust of this research is to advance statistical methodologies and theories for large-scale and high-dimensional inference with a particular focus on integrating potentially useful external covariate and structural information into inferential procedures. This research aims to develop innovative methodologies and theories to address several significant problems in large-scale and high-dimensional inference. In Project 1, the PI will introduce a new multiple testing procedure that can automatically select relevant covariates to improve the efficiency in inference when a large number of external covariates are available. In Project 2, the PI will develop a new multiple testing framework, which can integrate various forms of structural information. Because prior information is seldom perfectly accurate, a particular focus will be on developing procedures that are robust to misspecified/imperfect prior information. In Project 3, the PI shall propose new procedures for simultaneous inference in high-dimensional regressions with side information. The statistical tools will be used to identify skilled fund managers, assess the performance of climate field reconstructions, and analyze genomic data in an integrative way. Methods and computer code developed will be made publicly available.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.