IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v57y2013i1p223-232.html
   My bibliography  Save this article

Sparse sufficient dimension reduction using optimal scoring

Author

Listed:
  • Wang, Tao
  • Zhu, Lixing

Abstract

Sufficient dimension reduction is a body of theory and methods for reducing the dimensionality of predictors while preserving information on regressions. In this paper we propose a sparse dimension reduction method to perform interpretable dimension reduction. It is designed for situations in which the number of correlated predictors is very large relative to the sample size. The new procedure is based on the optimal scoring interpretation of the sliced inverse regression method. As a result, the regression framework of optimal scoring facilitates the use of commonly used regularization techniques. Simulation studies demonstrate the effectiveness and efficiency of the proposed approach.

Suggested Citation

  • Wang, Tao & Zhu, Lixing, 2013. "Sparse sufficient dimension reduction using optimal scoring," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 223-232.
    • Handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:223-232
    DOI: 10.1016/j.csda.2012.06.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947312002563
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2012.06.015?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    2. Lexin Li, 2007. "Sparse sufficient dimension reduction," Biometrika, Biometrika Trust, vol. 94(3), pages 603-613.
    3. Liqiang Ni & R. Dennis Cook & Chih-Ling Tsai, 2005. "A note on shrinkage sliced inverse regression," Biometrika, Biometrika Trust, vol. 92(1), pages 242-247, March.
    4. Yingcun Xia & Howell Tong & W. K. Li & Li‐Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410, August.
    5. Howard D. Bondell & Lexin Li, 2009. "Shrinkage inverse regression estimation for model‐free variable selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 287-299, January.
    6. Yin, Xiangrong & Li, Bing & Cook, R. Dennis, 2008. "Successive direction extraction for estimating the central subspace in a multiple-index regression," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1733-1757, September.
    7. Liping Zhu & Tao Wang & Lixing Zhu & Louis Ferré, 2010. "Sufficient dimension reduction through discretization-expectation estimation," Biometrika, Biometrika Trust, vol. 97(2), pages 295-304.
    8. Wang, Qin & Yin, Xiangrong, 2011. "Estimation of inverse mean: An orthogonal series approach," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1656-1664, April.
    9. Ye Z. & Weiss R.E., 2003. "Using the Bootstrap to Select One of a New Class of Dimension Reduction Methods," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 968-979, January.
    10. Cook, R. Dennis & Forzani, Liliana, 2009. "Likelihood-Based Sufficient Dimension Reduction," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 197-208.
    11. Dudoit S. & Fridlyand J. & Speed T. P, 2002. "Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 77-87, March.
    12. Li, Bing & Wang, Shaoli, 2007. "On Directional Regression for Dimension Reduction," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 997-1008, September.
    13. Lexin Li & R. Dennis Cook & Christopher J. Nachtsheim, 2005. "Model‐free variable selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 285-299, April.
    14. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    15. Lexin Li & Xiangrong Yin, 2008. "Sliced Inverse Regression with Regularizations," Biometrics, The International Biometric Society, vol. 64(1), pages 124-131, March.
    16. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhou, Jingke & Zhu, Lixing, 2016. "Principal minimax support vector machine for sufficient dimension reduction with contaminated data," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 33-48.

    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. Bilin Zeng & Xuerong Meggie Wen & Lixing Zhu, 2017. "A link-free sparse group variable selection method for single-index model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(13), pages 2388-2400, October.
    2. Weng, Jiaying, 2022. "Fourier transform sparse inverse regression estimators for sufficient variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    3. Yao, Weixin & Wang, Qin, 2013. "Robust variable selection through MAVE," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 42-49.
    4. Wang, Qin & Xue, Yuan, 2021. "An ensemble of inverse moment estimators for sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    5. Wang, Qin & Yin, Xiangrong, 2008. "A nonlinear multi-dimensional variable selection method for high dimensional data: Sparse MAVE," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4512-4520, May.
    6. Moradi Rekabdarkolaee, Hossein & Wang, Qin, 2017. "Variable selection through adaptive MAVE," Statistics & Probability Letters, Elsevier, vol. 128(C), pages 44-51.
    7. Wei Sun & Lexin Li, 2012. "Multiple Loci Mapping via Model-free Variable Selection," Biometrics, The International Biometric Society, vol. 68(1), pages 12-22, March.
    8. Zhou Yu & Yuexiao Dong & Li-Xing Zhu, 2016. "Trace Pursuit: A General Framework for Model-Free Variable Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 813-821, April.
    9. Yang Liu & Francesca Chiaromonte & Bing Li, 2017. "Structured Ordinary Least Squares: A Sufficient Dimension Reduction approach for regressions with partitioned predictors and heterogeneous units," Biometrics, The International Biometric Society, vol. 73(2), pages 529-539, June.
    10. Wang, Pei & Yin, Xiangrong & Yuan, Qingcong & Kryscio, Richard, 2021. "Feature filter for estimating central mean subspace and its sparse solution," Computational Statistics & Data Analysis, Elsevier, vol. 163(C).
    11. Fang, Fang & Yu, Zhou, 2020. "Model averaging assisted sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    12. Zifang Guo & Lexin Li & Wenbin Lu & Bing Li, 2015. "Groupwise Dimension Reduction via Envelope Method," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1515-1527, December.
    13. Wei Luo, 2022. "On efficient dimension reduction with respect to the interaction between two response variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 269-294, April.
    14. Zhou, Jingke & Zhu, Lixing, 2016. "Principal minimax support vector machine for sufficient dimension reduction with contaminated data," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 33-48.
    15. Changrong Yan & Dixin Zhang, 2013. "Sparse dimension reduction for survival data," Computational Statistics, Springer, vol. 28(4), pages 1835-1852, August.
    16. Wang, Tao & Xu, Pei-Rong & Zhu, Li-Xing, 2012. "Non-convex penalized estimation in high-dimensional models with single-index structure," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 221-235.
    17. Sheng, Wenhui & Yin, Xiangrong, 2013. "Direction estimation in single-index models via distance covariance," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 148-161.
    18. Yunquan Song & Zitong Li & Minglu Fang, 2022. "Robust Variable Selection Based on Penalized Composite Quantile Regression for High-Dimensional Single-Index Models," Mathematics, MDPI, vol. 10(12), pages 1-17, June.
    19. Yu, Zhou & Dong, Yuexiao & Huang, Mian, 2014. "General directional regression," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 94-104.
    20. Hilafu, Haileab & Yin, Xiangrong, 2013. "Sufficient dimension reduction in multivariate regressions with categorical predictors," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 139-147.

    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:eee:csdana:v:57:y:2013:i:1:p:223-232. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.