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Sparse Reduced-Rank Regression for Simultaneous Dimension Reduction and Variable Selection


  • Lisha Chen
  • Jianhua Z. Huang


The reduced-rank regression is an effective method in predicting multiple response variables from the same set of predictor variables. It reduces the number of model parameters and takes advantage of interrelations between the response variables and hence improves predictive accuracy. We propose to select relevant variables for reduced-rank regression by using a sparsity-inducing penalty. We apply a group-lasso type penalty that treats each row of the matrix of the regression coefficients as a group and show that this penalty satisfies certain desirable invariance properties. We develop two numerical algorithms to solve the penalized regression problem and establish the asymptotic consistency of the proposed method. In particular, the manifold structure of the reduced-rank regression coefficient matrix is considered and studied in our theoretical analysis. In our simulation study and real data analysis, the new method is compared with several existing variable selection methods for multivariate regression and exhibits competitive performance in prediction and variable selection.

Suggested Citation

  • Lisha Chen & Jianhua Z. Huang, 2012. "Sparse Reduced-Rank Regression for Simultaneous Dimension Reduction and Variable Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1533-1545, December.
  • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:500:p:1533-1545 DOI: 10.1080/01621459.2012.734178

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    References listed on IDEAS

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    7. Osmani, R.S., 1990. "Food Deprivation and Undernutrition in Rural Bangladesh," Research Paper 82, World Institute for Development Economics Research.
    8. Gerda Claeskens & Tatyana Krivobokova & Jean D. Opsomer, 2009. "Asymptotic properties of penalized spline estimators," Biometrika, Biometrika Trust, vol. 96(3), pages 529-544.
    9. Haerdle,Wolfgang & Bowman,Adrian, 1986. "Bootstrapping in nonparametric regression: Local adaptive smoothing and confidence bands," Discussion Paper Serie A 71, University of Bonn, Germany.
    10. M. Ruth & K. Donaghy & P. Kirshen, 2006. "Introduction," Chapters,in: Regional Climate Change and Variability, chapter 1 Edward Elgar Publishing.
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    Cited by:

    1. Fujikoshi, Yasunori & Sakurai, Tetsuro, 2016. "High-dimensional consistency of rank estimation criteria in multivariate linear model," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 199-212.
    2. Lian, Heng & Kim, Yongdai, 2016. "Nonconvex penalized reduced rank regression and its oracle properties in high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 383-393.
    3. Kharratzadeh, Milad & Coates, Mark, 2017. "Semi-parametric order-based generalized multivariate regression," Journal of Multivariate Analysis, Elsevier, vol. 156(C), pages 89-102.
    4. repec:eee:jmvana:v:157:y:2017:i:c:p:14-28 is not listed on IDEAS
    5. Wilms, Ines & Croux, Christophe, 2016. "Forecasting using sparse cointegration," International Journal of Forecasting, Elsevier, vol. 32(4), pages 1256-1267.
    6. Lian, Heng & Feng, Sanying & Zhao, Kaifeng, 2015. "Parametric and semiparametric reduced-rank regression with flexible sparsity," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 163-174.
    7. Luo, Ruiyan & Qi, Xin, 2017. "Signal extraction approach for sparse multivariate response regression," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 83-97.
    8. repec:eee:stapro:v:127:y:2017:i:c:p:173-177 is not listed on IDEAS
    9. repec:eee:csdana:v:112:y:2017:i:c:p:242-256 is not listed on IDEAS
    10. Feng, Sanying & Lian, Heng & Zhu, Fukang, 2016. "Reduced rank regression with possibly non-smooth criterion functions: An empirical likelihood approach," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 139-150.
    11. repec:bla:scjsta:v:44:y:2017:i:1:p:1-20 is not listed on IDEAS
    12. Kawano, Shuichi & Fujisawa, Hironori & Takada, Toyoyuki & Shiroishi, Toshihiko, 2015. "Sparse principal component regression with adaptive loading," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 192-203.
    13. Daniel Felix Ahelegbey, 2015. "The Econometrics of Networks: A Review," Working Papers 2015:13, Department of Economics, University of Venice "Ca' Foscari".

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