SPReM: Sparse Projection Regression Model For High-Dimensional Linear Regression

• 成果类型: Article
• 署名作者: Sun, Qiang; Zhu, Hongtu; Liu, Yufeng; Ibrahim, Joseph G.
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2014.892008
• 发表日期: 2015
• 页码: 289-302
• 关键词: principal-components; brain-development; MULTIVARIATE; CLASSIFICATION; fmri; heritability; CONVERGENCE; responses; selection; genetics

摘要

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 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 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.