FRG: Collaborative Research: Statistical Inference for High-Dimensional Data: Theory, Methodology and Applications

目前在科学调查中普遍出现的对高维数据集的分析提出了许多在较小规模的研究中不存在的统计挑战。从这样的数据中准确地提取信息变得越来越重要。FRG的这项建议是私人投资机构为应对紧迫的科学需求而共同努力的结果。具体地说，目标是开发一个全面的理论框架和一般方法，用于估计大型协方差矩阵及其泛函，以及用于预测因子和/或响应涉及功能测量的函数数据回归，并解决生物医学研究中的广泛重要应用。本提案中概述的统计和科学目标是一个迅速增长的统计和生物统计领域的智力中心。用于分析高维数据的新技术工具、推理程序和计算算法将极大地促进广泛学科的科学研究，这些领域包括天文学、生物、化学、生物信息学，特别是医学。所提出的高效分析方法在基于新的生物和遗传标记得出更准确的临床结果预测规则方面具有巨大的潜力，从而可能导致对疾病过程的更好理解。这项提案的研究结果将通过讲习班和系列研讨会传播，以便其他学科的研究人员可以公开使用这些方法。开发的软件工具将作为开放源代码免费公开提供。拟议的项目还将为学生和博士后研究人员带来高质量的培训。

The analysis of high-dimensional data sets now commonly arising in scientific investigations poses many statistical challenges not present in smaller scale studies. Extracting information with precision from such data is becoming ever more important. This FRG proposal is the PIs' unified effort to respond to the pressing scientific needs. Specifically, The goals are to develop a comprehensive theoretical framework and general methodologies for estimating a large covariance matrix and its functionals and for functional data regression where the predictors and/or the responses involve functional measurements, and to address a wide range of important applications in biomedical studies. The statistical and scientific objectives outlined in this proposal are at the intellectual center of a rapidly growing field in statistics and biostatistics. The new technical tools, inference procedures, and computing algorithms for analyzing high-dimensional data will greatly facilitate scientific investigations in a wide range of disciplines, These fields include astronomy, biology, chemistry, bioinformatics, and particularly in medicine. The proposed efficient analytical procedures hold great potential in deriving more accurate prediction rules for clinical outcomes based on new biological and genetic markers and thus may lead to a better understanding of disease processes. Research results from this proposal will be disseminated through the workshops and seminar series such that the methods would be publicly available to researchers in other disciplines. Software tools developed will be made freely and publicly available as open source code. The proposed project will also bring high-quality training to students and postdoctoral researchers.