IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v77y2014icp285-299.html
   My bibliography  Save this article

A new sliced inverse regression method for multivariate response

Author

Listed:
  • Coudret, R.
  • Girard, S.
  • Saracco, J.

Abstract

A semiparametric regression model of a q-dimensional multivariate response y on a p-dimensional covariate x is considered. A new approach is proposed based on sliced inverse regression (SIR) for estimating the effective dimension reduction (EDR) space without requiring a prespecified parametric model. The convergence at rate n of the estimated EDR space is shown. The choice of the dimension of the EDR space is discussed. Moreover, a way to cluster components of y related to the same EDR space is provided. Thus, the proposed multivariate SIR method can be used properly on each cluster instead of blindly applying it on all components of y. The numerical performances of multivariate SIR are illustrated on a simulation study. An application to the Minneapolis elementary schools data is also provided. Although the proposed methodology relies on SIR, it opens the door for new regression approaches with a multivariate response. They could be built similarly based on other reduction dimension methods.

Suggested Citation

  • Coudret, R. & Girard, S. & Saracco, J., 2014. "A new sliced inverse regression method for multivariate response," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 285-299.
    • Handle: RePEc:eee:csdana:v:77:y:2014:i:c:p:285-299
    DOI: 10.1016/j.csda.2014.03.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947314000838
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2014.03.006?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. 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.
    2. L. Barreda & A. Gannoun & Jérôme Saracco, 2007. "Some extensions of multivariate SIR," Post-Print hal-00153831, HAL.
    3. Scrucca, Luca, 2007. "Class prediction and gene selection for DNA microarrays using regularized sliced inverse regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 438-451, September.
    4. Luke A. Prendergast, 2007. "Implications of influence function analysis for sliced inverse regression and sliced average variance estimation," Biometrika, Biometrika Trust, vol. 94(3), pages 585-601.
    5. Zhu, Lixing & Miao, Baiqi & Peng, Heng, 2006. "On Sliced Inverse Regression With High-Dimensional Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 630-643, June.
    6. L. A. Prendergast, 2005. "Influence Functions for Sliced Inverse Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(3), pages 385-404, September.
    7. C. Bernard‐Michel & L. Gardes & S. Girard, 2008. "A Note on Sliced Inverse Regression with Regularizations," Biometrics, The International Biometric Society, vol. 64(3), pages 982-984, September.
    8. Zhu, Li-Ping & Zhu, Li-Xing & Feng, Zheng-Hui, 2010. "Dimension Reduction in Regressions Through Cumulative Slicing Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1455-1466.
    9. Barrios, M. Pilar & Velilla, Santiago, 2007. "A bootstrap method for assessing the dimension of a general regression problem," Statistics & Probability Letters, Elsevier, vol. 77(3), pages 247-255, February.
    10. Hino, Hideitsu & Wakayama, Keigo & Murata, Noboru, 2013. "Entropy-based sliced inverse regression," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 105-114.
    11. Bai, Z. D. & He, Xuming, 2004. "A chi-square test for dimensionality with non-Gaussian data," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 109-117, January.
    12. Guy Nkiet, 2008. "Consistent estimation of the dimensionality in sliced inverse regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(2), pages 257-271, June.
    13. Benoît Liquet & Jérôme Saracco, 2012. "A graphical tool for selecting the number of slices and the dimension of the model in SIR and SAVE approaches," Computational Statistics, Springer, vol. 27(1), pages 103-125, March.
    14. Li, Bing & Wen, Songqiao & Zhu, Lixing, 2008. "On a Projective Resampling Method for Dimension Reduction With Multivariate Responses," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1177-1186.
    15. Amato, U. & Antoniadis, A. & De Feis, I., 2006. "Dimension reduction in functional regression with applications," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2422-2446, May.
    16. Gannoun, Ali & Girard, Stephane & Guinot, Christiane & Saracco, Jerome, 2004. "Sliced inverse regression in reference curves estimation," Computational Statistics & Data Analysis, Elsevier, vol. 46(1), pages 103-122, May.
    17. Efstathia Bura & R. Dennis Cook, 2001. "Estimating the structural dimension of regressions via parametric inverse regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 393-410.
    18. Scrucca, Luca, 2011. "Model-based SIR for dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 3010-3026, November.
    19. Aragon, Y. & Saracco, J., 1996. "Sliced Inverse Regression (SIR): An Appraisal of Small Sample Alternatives to Slicing," Papers 95.392, Toulouse - GREMAQ.
    20. Saracco, Jérôme, 2005. "Asymptotics for pooled marginal slicing estimator based on SIR[alpha] approach," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 117-135, September.
    21. Zhu, Li-Xing & Ohtaki, Megu & Li, Yingxing, 2007. "On hybrid methods of inverse regression-based algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2621-2635, February.
    22. Lexin Li & Xiangrong Yin, 2008. "Sliced Inverse Regression with Regularizations," Biometrics, The International Biometric Society, vol. 64(1), pages 124-131, March.
    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. Bousebata, Meryem & Enjolras, Geoffroy & Girard, Stéphane, 2023. "Extreme partial least-squares," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    2. Girard, Stéphane & Lorenzo, Hadrien & Saracco, Jérôme, 2022. "Advanced topics in Sliced Inverse Regression," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    3. Zhang, Hong-Fan, 2021. "Minimum Average Variance Estimation with group Lasso for the multivariate response Central Mean Subspace," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    4. Chiancone, Alessandro & Forbes, Florence & Girard, Stéphane, 2017. "Student Sliced Inverse Regression," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 441-456.

    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. Girard, Stéphane & Lorenzo, Hadrien & Saracco, Jérôme, 2022. "Advanced topics in Sliced Inverse Regression," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    2. Marie Chavent & Stéphane Girard & Vanessa Kuentz-Simonet & Benoit Liquet & Thi Nguyen & Jérôme Saracco, 2014. "A sliced inverse regression approach for data stream," Computational Statistics, Springer, vol. 29(5), pages 1129-1152, October.
    3. Benoît Liquet & Jérôme Saracco, 2012. "A graphical tool for selecting the number of slices and the dimension of the model in SIR and SAVE approaches," Computational Statistics, Springer, vol. 27(1), pages 103-125, March.
    4. Weng, Jiaying, 2022. "Fourier transform sparse inverse regression estimators for sufficient variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    5. Kim, Kyongwon, 2022. "On principal graphical models with application to gene network," Computational Statistics & Data Analysis, Elsevier, vol. 166(C).
    6. Dong, Yuexiao & Yu, Zhou & Zhu, Liping, 2015. "Robust inverse regression for dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 134(C), pages 71-81.
    7. Chiancone, Alessandro & Forbes, Florence & Girard, Stéphane, 2017. "Student Sliced Inverse Regression," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 441-456.
    8. Xie, Chuanlong & Zhu, Lixing, 2019. "A goodness-of-fit test for variable-adjusted models," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 27-48.
    9. 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.
    10. Zeng, Bilin & Yu, Zhou & Wen, Xuerong Meggie, 2015. "A note on cumulative mean estimation," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 322-327.
    11. Chen, Canyi & Xu, Wangli & Zhu, Liping, 2022. "Distributed estimation in heterogeneous reduced rank regression: With application to order determination in sufficient dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    12. 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).
    13. Guochang Wang & Jianjun Zhou & Wuqing Wu & Min Chen, 2017. "Robust functional sliced inverse regression," Statistical Papers, Springer, vol. 58(1), pages 227-245, March.
    14. Ming-Yueh Huang & Chin-Tsang Chiang, 2017. "An Effective Semiparametric Estimation Approach for the Sufficient Dimension Reduction Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1296-1310, July.
    15. Wang, Qin & Xue, Yuan, 2021. "An ensemble of inverse moment estimators for sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    16. Prendergast, Luke A. & Smith, Jodie A., 2022. "Influence functions for linear discriminant analysis: Sensitivity analysis and efficient influence diagnostics," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    17. Wenjuan Li & Wenying Wang & Jingsi Chen & Weidong Rao, 2023. "Aggregate Kernel Inverse Regression Estimation," Mathematics, MDPI, vol. 11(12), pages 1-10, June.
    18. Pircalabelu, Eugen & Artemiou, Andreas, 2021. "Graph informed sliced inverse regression," Computational Statistics & Data Analysis, Elsevier, vol. 164(C).
    19. Deng, Jianqiu & Yang, Xiaojie & Wang, Qihua, 2022. "Surrogate space based dimension reduction for nonignorable nonresponse," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    20. Zhang, Hong-Fan, 2021. "Minimum Average Variance Estimation with group Lasso for the multivariate response Central Mean Subspace," Journal of Multivariate Analysis, Elsevier, vol. 184(C).

    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:77:y:2014:i:c:p:285-299. 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.