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Variable selection in high-dimensional sparse multiresponse linear regression models

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  • Shan Luo

    (Shanghai Jiao Tong University)

Abstract

We consider variable selection in high-dimensional sparse multiresponse linear regression models, in which a q-dimensional response vector has a linear relationship with a p-dimensional covariate vector through a sparse coefficient matrix $$B\in R^{p\times q}$$B∈Rp×q. We propose a consistent procedure for the purpose of identifying the nonzeros in B. The procedure consists of two major steps, where the first step focuses on the detection of all the nonzero rows in B, the latter aims to further discover its individual nonzero cells. The first step is an extension of Orthogonal Matching Pursuit (OMP) and the second step adopts the bootstrap strategy. The theoretical property of our proposed procedure is established. Extensive numerical studies are presented to compare its performances with available representatives.

Suggested Citation

  • Shan Luo, 2020. "Variable selection in high-dimensional sparse multiresponse linear regression models," Statistical Papers, Springer, vol. 61(3), pages 1245-1267, June.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:3:d:10.1007_s00362-018-0989-x
    DOI: 10.1007/s00362-018-0989-x
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    References listed on IDEAS

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    1. Simila, Timo & Tikka, Jarkko, 2007. "Input selection and shrinkage in multiresponse linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 406-422, September.
    2. Hyonho Chun & Sündüz Keleş, 2010. "Sparse partial least squares regression for simultaneous dimension reduction and variable selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 3-25, January.
    3. Shan Luo & Zehua Chen, 2014. "Sequential Lasso Cum EBIC for Feature Selection With Ultra-High Dimensional Feature Space," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1229-1240, September.
    4. T. Tony Cai & Hongzhe Li & Weidong Liu & Jichun Xie, 2013. "Covariate-adjusted precision matrix estimation with an application in genetical genomics," Biometrika, Biometrika Trust, vol. 100(1), pages 139-156.
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