title: SPReM: Sparse Projection Regression Model For High-dimensional Linear Regression.
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'sT2test 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.
authors.affiliation: Department of Biostatistics, University of North Carolina at Chapel Hill, NC 27599-7420.
authors.forename: Qiang
authors.initials: Q
authors.lastname: Sun
authors.affiliation: Department of Biostatistics, University of North Carolina at Chapel Hill, NC 27599-7420.
authors.forename: Hongtu
authors.initials: H
authors.lastname: Zhu
authors.affiliation: Department of Statistics and Operation Research, University of North Carolina at Chapel Hill, CB 3260, Chapel Hill, NC 27599.
authors.forename: Yufeng
authors.initials: Y
authors.lastname: Liu
authors.affiliation: Department of Biostatistics, University of North Carolina at Chapel Hill, NC 27599-7420.
authors.forename: Joseph G
authors.initials: JG
authors.lastname: Ibrahim
keywords: heritability ratio; imaging genetics; multivariate regression; projection regression; sparse; wild bootstrap