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

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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.