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6741119 
Journal Article 
SPReM: Sparse Projection Regression Model For High-Dimensional Linear Regression 
Sun, Q; Zhu, H; Liu, Y; Ibrahim, JG 
2015 
Yes 
Journal of the American Statistical Association
ISSN: 0162-1459
EISSN: 1537-274X 
110 
509 
289-302 
English 
26527844 
WOS:000353474200023 
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 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 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. 
Heritability ratio; Imaging genetics; Multivariate regression; Projection regression; Sparse; Wild bootstrap