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

高维数据集的分析，现在通常出现在科学调查带来了许多统计上的挑战，不存在于较小规模的研究。从这些数据中精确地提取信息变得越来越重要。这个联邦政府的建议是PI的统一努力，以应对迫切的科学需求。具体来说，我们的目标是开发一个全面的理论框架和一般方法，估计一个大的协方差矩阵和它的功能和功能数据回归的预测和/或响应涉及功能测量，并解决广泛的重要应用在生物医学研究。 本提案中概述的统计和科学目标是统计和生物统计学快速发展领域的知识中心。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、生物学、化学、生物信息学，特别是医学。所提出的有效的分析程序具有很大的潜力，在推导出更准确的预测规则的基础上，新的生物和遗传标记的临床结果，从而可能会导致更好地了解疾病的过程。这一建议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获得这些方法。所开发的软件工具将作为开放源码免费向公众提供。拟议的项目还将为学生和博士后研究人员提供高质量的培训。

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.