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A two-stage sequential conditional selection approach to sparse high-dimensional multivariate regression models

Author

Listed:
  • Zehua Chen

    (National University of Singapore)

  • Yiwei Jiang

    (National University of Singapore)

Abstract

In this article, we deal with sparse high-dimensional multivariate regression models. The models distinguish themselves from ordinary multivariate regression models in two aspects: (1) the dimension of the response vector and the number of covariates diverge to infinity; (2) the nonzero entries of the coefficient matrix and the precision matrix are sparse. We develop a two-stage sequential conditional selection (TSCS) approach to the identification and estimation of the nonzeros of the coefficient matrix and the precision matrix. It is established that the TSCS is selection consistent for the identification of the nonzeros of both the coefficient matrix and the precision matrix. Simulation studies are carried out to compare TSCS with the existing state-of-the-art methods, which demonstrates that the TSCS approach outperforms the existing methods. As an illustration, the TSCS approach is also applied to a real dataset.

Suggested Citation

  • Zehua Chen & Yiwei Jiang, 2020. "A two-stage sequential conditional selection approach to sparse high-dimensional multivariate regression models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 65-90, February.
    • Handle: RePEc:spr:aistmt:v:72:y:2020:i:1:d:10.1007_s10463-018-0686-5
    DOI: 10.1007/s10463-018-0686-5
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    References listed on IDEAS

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    1. Jiahua Chen & Zehua Chen, 2008. "Extended Bayesian information criteria for model selection with large model spaces," Biometrika, Biometrika Trust, vol. 95(3), pages 759-771.
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    6. Lee, Wonyul & Liu, Yufeng, 2012. "Simultaneous multiple response regression and inverse covariance matrix estimation via penalized Gaussian maximum likelihood," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 241-255.
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