IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v101y2010i1p271-290.html
   My bibliography  Save this article

An integral transform method for estimating the central mean and central subspaces

Author

Listed:
  • Zeng, Peng
  • Zhu, Yu

Abstract

The central mean and central subspaces of generalized multiple index model are the main inference targets of sufficient dimension reduction in regression. In this article, we propose an integral transform (ITM) method for estimating these two subspaces. Applying the ITM method, estimates are derived, separately, for two scenarios: (i) No distributional assumptions are imposed on the predictors, and (ii) the predictors are assumed to follow an elliptically contoured distribution. These estimates are shown to be asymptotically normal with the usual root-n convergence rate. The ITM method is different from other existing methods in that it avoids estimation of the unknown link function between the response and the predictors and it does not rely on distributional assumptions of the predictors under scenario (i) mentioned above.

Suggested Citation

  • Zeng, Peng & Zhu, Yu, 2010. "An integral transform method for estimating the central mean and central subspaces," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 271-290, January.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:1:p:271-290
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(09)00147-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Zhu, Yu & Zeng, Peng, 2006. "Fourier Methods for Estimating the Central Subspace and the Central Mean Subspace in Regression," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1638-1651, December.
    2. 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.
    3. Collomb, Gérard & Härdle, Wolfgang, 1986. "Strong uniform convergence rates in robust nonparametric time series analysis and prediction: Kernel regression estimation from dependent observations," Stochastic Processes and their Applications, Elsevier, vol. 23(1), pages 77-89, October.
    4. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    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. 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.
    2. Tao, Chenyang & Feng, Jianfeng, 2017. "Canonical kernel dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 131-148.
    3. S. Yaser Samadi & Tharindu P. De Alwis, 2023. "Fourier Methods for Sufficient Dimension Reduction in Time Series," Papers 2312.02110, arXiv.org.
    4. Wu, Runxiong & Chen, Xin, 2021. "MM algorithms for distance covariance based sufficient dimension reduction and sufficient variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    5. Tianqing Liu & Danning Li & Fengjiao Ren & Jianguo Sun & Xiaohui Yuan, 2024. "A new sufficient dimension reduction method via rank divergence," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(3), pages 921-950, September.
    6. Zeng, Peng, 2011. "A link-free method for testing the significance of predictors," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 550-562, March.
    7. 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.

    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. 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.
    2. 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).
    3. Aradillas-Lopez, Andres, 2012. "Pairwise-difference estimation of incomplete information games," Journal of Econometrics, Elsevier, vol. 168(1), pages 120-140.
    4. S. Yaser Samadi & Tharindu P. De Alwis, 2023. "Fourier Methods for Sufficient Dimension Reduction in Time Series," Papers 2312.02110, arXiv.org.
    5. Wang, Qin & Xue, Yuan, 2021. "An ensemble of inverse moment estimators for sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    6. Lewbel, Arthur, 1995. "Consistent nonparametric hypothesis tests with an application to Slutsky symmetry," Journal of Econometrics, Elsevier, vol. 67(2), pages 379-401, June.
    7. Arthur Lewbel, 2000. "Asymptotic Trimming for Bounded Density Plug-in Estimators," Boston College Working Papers in Economics 479, Boston College Department of Economics, revised 30 Oct 2000.
    8. Burton Hollifield & Robert A. Miller & Patrik Sandås, 2004. "Empirical Analysis of Limit Order Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(4), pages 1027-1063.
    9. Zhang, Jing & Wang, Qin & Mays, D'Arcy, 2021. "Robust MAVE through nonconvex penalized regression," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    10. repec:jss:jstsof:39:i03 is not listed on IDEAS
    11. Lee, Myoung-jae & Vella, Francis, 2006. "A semi-parametric estimator for censored selection models with endogeneity," Journal of Econometrics, Elsevier, vol. 130(2), pages 235-252, February.
    12. Zhu, Li-Ping & Yu, Zhou & Zhu, Li-Xing, 2010. "A sparse eigen-decomposition estimation in semiparametric regression," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 976-986, April.
    13. 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.
    14. Zhu, Liping & Zhong, Wei, 2015. "Estimation and inference on central mean subspace for multivariate response data," Computational Statistics & Data Analysis, Elsevier, vol. 92(C), pages 68-83.
    15. Zhu, Xuehu & Chen, Fei & Guo, Xu & Zhu, Lixing, 2016. "Heteroscedasticity testing for regression models: A dimension reduction-based model adaptive approach," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 263-283.
    16. Aradillas-Lopez, Andres, 2010. "Semiparametric estimation of a simultaneous game with incomplete information," Journal of Econometrics, Elsevier, vol. 157(2), pages 409-431, August.
    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. Xue, Yuan & Zhang, Nan & Yin, Xiangrong & Zheng, Haitao, 2017. "Sufficient dimension reduction using Hilbert–Schmidt independence criterion," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 67-78.
    19. Yao, Weixin & Wang, Qin, 2013. "Robust variable selection through MAVE," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 42-49.
    20. Iaci, Ross & Yin, Xiangrong & Zhu, Lixing, 2016. "The Dual Central Subspaces in dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 178-189.
    21. Zhao, Junlong & Zhao, Xiuli, 2010. "Dimension reduction using the generalized gradient direction," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1089-1102, April.

    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:jmvana:v:101:y:2010:i:1:p:271-290. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.