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SPReM: Sparse Projection Regression Model for High-dimensional Linear Regression

Institution:
1Department of Biostatistics, University of North Carolina at Chapel Hill, NC, USA.
2Department of Statistics and Operation Research, University of North Carolina at Chapel Hill, NC, USA.
Publication Date:
Nov-2015
Journal:
J Am Stat Assoc
Volume Number:
110
Issue Number:
509
Pages:
289-302
Citation:
J Am Stat Assoc. 2015 Nov;110(509):289-302.
PubMed ID:
26527844
PMCID:
PMC4627720
Keywords:
heritability ratio, imaging genetics, multivariate regression, projection regression, sparse, wild bootstrap
Appears in Collections:
NA-MIC
Sponsors:
U54 EB005149/EB/NIBIB NIH HHS/United States
R01 CA074015/CA/NCI NIH HHS/United States
R01 CA149569/CA/NCI NIH HHS/United States
R01 GM070335/GM/NIGMS NIH HHS/United States
R01 MH086633/MH/NIMH NIH HHS/United States
R21 AG033387/AG/NIA NIH HHS/United States
U01 AG024904/AG/NIA NIH HHS/United States
UL1 RR025747/RR/NCRR NIH HHS/United States
UL1 TR001111/TR/NCATS NIH HHS/United States
Generated Citation:
Sun Q., Zhu H., Liu Y., Ibrahim J.G. SPReM: Sparse Projection Regression Model for High-dimensional Linear Regression. J Am Stat Assoc. 2015 Nov;110(509):289-302. PMID: 26527844. PMCID: PMC4627720.
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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 T 2 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.

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