IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1803.07247.html
   My bibliography  Save this paper

Sparse Reduced Rank Regression With Nonconvex Regularization

Author

Listed:
  • Ziping Zhao
  • Daniel P. Palomar

Abstract

In this paper, the estimation problem for sparse reduced rank regression (SRRR) model is considered. The SRRR model is widely used for dimension reduction and variable selection with applications in signal processing, econometrics, etc. The problem is formulated to minimize the least squares loss with a sparsity-inducing penalty considering an orthogonality constraint. Convex sparsity-inducing functions have been used for SRRR in literature. In this work, a nonconvex function is proposed for better sparsity inducing. An efficient algorithm is developed based on the alternating minimization (or projection) method to solve the nonconvex optimization problem. Numerical simulations show that the proposed algorithm is much more efficient compared to the benchmark methods and the nonconvex function can result in a better estimation accuracy.

Suggested Citation

  • Ziping Zhao & Daniel P. Palomar, 2018. "Sparse Reduced Rank Regression With Nonconvex Regularization," Papers 1803.07247, arXiv.org.
    • Handle: RePEc:arx:papers:1803.07247
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1803.07247
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Zhou, Guofu, 1995. "Small sample rank tests with applications to asset pricing," Journal of Empirical Finance, Elsevier, vol. 2(1), pages 71-93, March.
    2. Bekker, Paul & Dobbelstein, Pascal & Wansbeek, Tom, 1996. "The APT Model as Reduced-Rank Regression," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 199-202, April.
    3. Izenman, Alan Julian, 1975. "Reduced-rank regression for the multivariate linear model," Journal of Multivariate Analysis, Elsevier, vol. 5(2), pages 248-264, June.
    4. Ziping Zhao & Daniel P. Palomar, 2017. "Robust Maximum Likelihood Estimation of Sparse Vector Error Correction Model," Papers 1710.05513, arXiv.org.
    5. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    6. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
    7. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Canhong Wen & Zhenduo Li & Ruipeng Dong & Yijin Ni & Wenliang Pan, 2023. "Simultaneous Dimension Reduction and Variable Selection for Multinomial Logistic Regression," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1044-1060, September.
    2. Goh, Gyuhyeong & Dey, Dipak K. & Chen, Kun, 2017. "Bayesian sparse reduced rank multivariate regression," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 14-28.
    3. 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.
    4. Takumi Saegusa & Tianzhou Ma & Gang Li & Ying Qing Chen & Mei-Ling Ting Lee, 2020. "Variable Selection in Threshold Regression Model with Applications to HIV Drug Adherence Data," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 12(3), pages 376-398, December.
    5. Dong, Ruipeng & Li, Daoji & Zheng, Zemin, 2021. "Parallel integrative learning for large-scale multi-response regression with incomplete outcomes," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    6. Xing Gao & Sungwon Lee & Gen Li & Sungkyu Jung, 2021. "Covariate‐driven factorization by thresholding for multiblock data," Biometrics, The International Biometric Society, vol. 77(3), pages 1011-1023, September.
    7. Dmitry Kobak & Yves Bernaerts & Marissa A. Weis & Federico Scala & Andreas S. Tolias & Philipp Berens, 2021. "Sparse reduced‐rank regression for exploratory visualisation of paired multivariate data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(4), pages 980-1000, August.
    8. Hu, Jianhua & Liu, Xiaoqian & Liu, Xu & Xia, Ningning, 2022. "Some aspects of response variable selection and estimation in multivariate linear regression," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    9. 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.
    10. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    11. Jun Yan & Jian Huang, 2012. "Model Selection for Cox Models with Time-Varying Coefficients," Biometrics, The International Biometric Society, vol. 68(2), pages 419-428, June.
    12. Shuichi Kawano, 2014. "Selection of tuning parameters in bridge regression models via Bayesian information criterion," Statistical Papers, Springer, vol. 55(4), pages 1207-1223, November.
    13. Peng, Heng & Lu, Ying, 2012. "Model selection in linear mixed effect models," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 109-129.
    14. Yize Zhao & Matthias Chung & Brent A. Johnson & Carlos S. Moreno & Qi Long, 2016. "Hierarchical Feature Selection Incorporating Known and Novel Biological Information: Identifying Genomic Features Related to Prostate Cancer Recurrence," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1427-1439, October.
    15. G. Aneiros & P. Vieu, 2016. "Sparse nonparametric model for regression with functional covariate," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(4), pages 839-859, October.
    16. Bura, Efstathia & Cook, R. Dennis, 2003. "Rank estimation in reduced-rank regression," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 159-176, October.
    17. Lam, Clifford, 2008. "Estimation of large precision matrices through block penalization," LSE Research Online Documents on Economics 31543, London School of Economics and Political Science, LSE Library.
    18. Pradeep Ravikumar & John Lafferty & Han Liu & Larry Wasserman, 2009. "Sparse additive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 1009-1030, November.
    19. Zhang, Tao & Zhang, Qingzhao & Wang, Qihua, 2014. "Model detection for functional polynomial regression," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 183-197.
    20. Toshio Honda, 2021. "The de-biased group Lasso estimation for varying coefficient models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(1), pages 3-29, February.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1803.07247. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.