CAREER: High-Dimensional M-Estimation Under Nonstandard Conditions

基因组学、医学研究和神经科学方面的现代技术产生了大量数据，这需要可靠的统计分析工具。虽然在过去的几十年里，统计学和数据科学领域对大数据分析的研究活动激增，但由于数据结构的复杂性或现代应用中收集数据的方式，现有的统计工具不足以产生可靠的结果。该项目将开发新的统计和计算工具，以解决现代大数据中出现的挑战，并在软件包中实施。该项目将使包括生物学家、流行病学家、医生和神经科学家在内的广泛研究人员受益。这项研究还辅之以同样重要的教育和推广计划，包括设计新的本科和研究生课程，并招募未被充分代表的少数民族参加夏季研究项目。本项目将开发一种新的计算和统计框架，用于两种非标准条件下的高维m估计。在第一个项目中，首席研究员将考虑具有非光滑损失函数（例如指标函数）的高维m估计。损失函数的不连续导致理论的不规范，需要新的统计方法配备更精细的理论分析。在第二个项目中，首席研究员将考虑受测量约束的m估计，因为结果只收集在大数据集的一个非常小的子集中。首席研究员将开发可扩展的计算算法和统计有效的估计/推理程序。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。

Modern technology in genomics, medical research and neuroscience generates enormous amounts of data, which calls for reliable statistical analysis tools. While the past decades have witnessed a surge of research activities on the analysis of big data in statistics and data science, the existing statistical tools are not adequate to produce reliable results due to the complexity of the data structure or the manner in which the data are collected in modern applications. The project will develop novel statistical and computational tools to address the emerging challenges in modern big data and implement them within software packages. The project will benefit a broad range of researchers including biologists, epidemiologists, medical doctors and neuroscientists. The research is complemented by an equally important education and outreach plan including designing new undergraduate and graduate courses and recruiting underrepresented minorities into the summer research program. This project will develop a novel computational and statistical framework for high-dimensional M-estimation under two types of nonstandard conditions. In the first project, the principal investigator will consider high-dimensional M-estimation with non-smooth loss functions (e.g. indicator function). The discontinuity of the loss function leads to nonstandard theory and requires new statistical methods equipped with more refined theoretical analysis. In the second project, the principal investigator will consider M-estimation subject to measurement constraints in the sense that the outcomes are only collected in a very small subset of a big dataset. The principal investigator will develop scalable computational algorithms and statistically valid estimation/inference procedures.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.