Robust Post-Selection Inference with Application to Subgroup Analysis

研究人员一直面临着来自高维数据的挑战，这些数据包含每个受试者的许多不同特征。例如，生物医学科学家分析数以万计的基因组，以确定疾病的原因，并找到最有希望的治疗方法；社会科学家通过利用从社交媒体收集的大量个人数据来研究不同的政策影响。该项目列出了两条研究路线，目的是在这一具有挑战性的环境中发展有效的统计推断。从这个项目开发的洞察力和工具将有助于推进广泛的其他学科，包括经济、教育、医疗保健和生物医学科学。此外，研究生将参与研究统计保证的项目，并为研究开发相关软件包。由于该项目开发了具有实质性应用的现代统计方法，它将适合培养具有广泛技能的研究生。该项目解决了两个研究问题，并试图为更明智的高维度决策提供见解、理论和工具。第一个问题是研究治疗效果的异质性。在高维协变量存在的情况下，异质性治疗效果的量化和表征在评估社会计划和医疗的有效性方面发挥着越来越重要的作用。特别是，这项研究将开发有效的程序，通过协变量平衡来估计不同分位数处理效果和亚组平均处理效果。第二个问题是研究数据分割对高维数据进行推理的有效性和无效性。该项目将解决在虚拟/不平衡变量数量较多时估计回归系数时的“随机分裂偏差”问题。为了克服这一挑战，该项目将开发一个指导性数据拆分框架，将数据拆分成更平衡的两部分。由于随机数据拆分的使用超出了选择后推理的范围，所开发的框架及其衍生的可能解决方案广泛适用于许多数据驱动的调查。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。

Researchers have been facing challenges from high-dimensional data that contain many different characteristics for each subject. For example, biomedical scientists analyze tens of thousands of genomes to determine the cause of disease and find the most promising treatments; social scientists study differential policy impacts by leveraging vast amounts of personal data gathered from social media. This project lays out two lines of research aimed at developing valid statistical inference in this challenging environment. The insights and tools developed from this project would contribute to the advancement of a wide variety of other disciplines, including economics, education, health care, and biomedical sciences. In addition, graduate students will be engaged in the project to study the statistical guarantees and to develop relevant software packages for the research. Since the project develops modern statistical methodologies with substantial applications, it will be suitable for training graduate students with a broad range of skills.This project addresses two research problems and seeks to provide insights, theory and tools for more informed decision making in high dimensions. The first problem focuses on studying the treatment effect heterogeneity. Quantification and characterization of heterogeneous treatment effects play an increasingly important role in evaluating the efficacy of social programs and medical treatments in the presence of high-dimensional covariates. In particular, the research will develop efficient procedures for estimating heterogeneous quantile treatment effects and subgroup average treatment effects via covariate balancing. The second problem focuses on studying the validity and invalidity of data splitting for conducting inference with high-dimensional data. The project will address the issue of “random-splitting bias” in estimating the regression coefficients when the number of dummy/imbalanced variables is sizable. To overcome this challenge, the project will develop a guided data splitting framework that splits the data into more balanced halves. Because the usage of random data splitting goes beyond post-selection inference, the framework developed and the possible solutions derived from it are broadly applicable to many data-driven investigations.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.