Title | SPReM: Sparse Projection Regression Model For High-dimensional Linear Regression. |
Publication Type | Journal Article |
Year of Publication | 2015 |
Authors | Sun, Qiang, Hongtu Zhu, Yufeng Liu, and Joseph G. Ibrahim |
Corporate Authors | Alzheimer’;s Disease Neuroimaging Initiative |
Journal | J Am Stat Assoc |
Volume | 110 |
Issue | 509 |
Pagination | 289-302 |
Date Published | 2015 |
ISSN | 0162-1459 |
Abstract | The aim of this paper 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 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 multi-rank 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 out-performs other state-of-the-art methods. |
DOI | 10.1080/01621459.2014.892008 |
Alternate Journal | J Am Stat Assoc |
Original Publication | SPReM: Sparse projection regression model for high-dimensional linear regression. |
PubMed ID | 26527844 |
PubMed Central ID | PMC4627720 |
Grant List | K01 AG030514 / AG / NIA NIH HHS / United States UL1 TR001111 / TR / NCATS NIH HHS / United States U01 AG024904 / AG / NIA NIH HHS / United States U54 EB005149 / EB / NIBIB NIH HHS / United States R01 MH086633 / MH / NIMH NIH HHS / United States R01 GM070335 / GM / NIGMS NIH HHS / United States R01 CA149569 / CA / NCI NIH HHS / United States UL1 RR025747 / RR / NCRR NIH HHS / United States P30 AG010129 / AG / NIA NIH HHS / United States P01 CA142538 / CA / NCI NIH HHS / United States R21 AG033387 / AG / NIA NIH HHS / United States R01 CA074015 / CA / NCI NIH HHS / United States |
SPReM: Sparse Projection Regression Model For High-dimensional Linear Regression.
Project: