SPReM: Sparse Projection Regression Model For High-Dimensional Linear Regression
Year: 2015
Type: article
Abstract: The aim of this article is to develop a sparse projection regression modeling (SPReM) framework to perform multivariate regression modeling with a large number of responses and a multivariate covariate of interest. We propose two novel heritability ratios to simultaneously perform dimension reduction, response selection, estimation, and testing, while explicitly accounting for correlations among multivariate responses. Our SPReM is devised to specifically address the low statistical power issue of many standard statistical approaches, such as the Hotelling’s T2 test statistic or a mass univariate analysis, for high-dimensional data. We formulate the estimation problem of SPReM as a novel sparse unit rank projection (SURP) problem and propose a fast optimization algorithm for SURP. Furthermore, we extend SURP to the sparse multirank projection (SMURP) by adopting a sequential SURP approximation. Theoretically, we have systematically investigated the convergence properties of SURP and the convergence rate of SURP estimates. Our simulation results and real data analysis have shown that SPReM outperforms other state-of-the-art methods.
Institution: University of North Carolina at Chapel Hill
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funders: National Science Foundation, Alzheimer's Association, Bristol-Myers Squibb, Eli Lilly and Company, Biogen, F. Hoffmann-La Roche, Alzheimer's Disease Neuroimaging Initiative, BioClinica, Eisai, National Institutes of Health, Genentech, National Institute on Aging, National Institute of Mental Health, National Cancer Institute, National Institute of General Medical Sciences, National Institute of Biomedical Imaging and Bioengineering, National Center for Research Resources, National Center for Advancing Translational Sciences
Awards: G104586243, UC Davis Alzheimer's Disease Core Center, Alzheimer's Disease Neuroimaging Initiative, G2340207221, G244020180, G2835601961, G29951154, G3131374986, G3553156159, G3710456697, G3797919405, G3870774570, G3966393351, "MR Morphometrics and Cognitive Decline Rate in Large-Scale Aging Studies", North Carolina Translational & Clinical Sciences Institute (NC TraCS), National Alliance for Medical Image Computing (NAMIC), G43180419, Statistical Methods for Cancer Clinical Trials, G5159369687, G5207404921, G5654639750, G6210868510, Statistical Analysis of Biomedical Imaging Data in Curved Space, G6371410416, G6412110892, UNC Clinical and Translational Science Award, G6899163935, G6948409098, G781725486, G8301434335, Longitudinal Analysis of Biomedical Imaging Data, Flexible statistical machine learning techniques for cancer-related data, Inference in Regression Models with Missing Covariates, G8918007943, Bayesian Approaches to Model Selection for Survival Data, G9000039018, G9000099481, G9000116110, G9000122335, G9000169796, G9000198256
OpenAlex ID: W2123553417