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

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  • Qiang Sun
  • Hongtu Zhu
  • Yufeng Liu
  • Joseph G. Ibrahim

Abstract

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 -super-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.

Suggested Citation

  • Qiang Sun & Hongtu Zhu & Yufeng Liu & Joseph G. Ibrahim, 2015. "SPReM: Sparse Projection Regression Model For High-Dimensional Linear Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 289-302, March.
    • Handle: RePEc:taf:jnlasa:v:110:y:2015:i:509:p:289-302
    DOI: 10.1080/01621459.2014.892008
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    References listed on IDEAS

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    Cited by:

    1. Christis Katsouris, 2023. "High Dimensional Time Series Regression Models: Applications to Statistical Learning Methods," Papers 2308.16192, arXiv.org.
    2. Yeonhee Park & Zhihua Su & Hongtu Zhu, 2017. "Groupwise envelope models for imaging genetic analysis," Biometrics, The International Biometric Society, vol. 73(4), pages 1243-1253, December.

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