IDEAS home Printed from https://ideas.repec.org/a/oup/biomet/v100y2013i2p371-383.html
   My bibliography  Save this article

Efficiency loss and the linearity condition in dimension reduction

Author

Listed:
  • Yanyuan Ma
  • Liping Zhu

Abstract

Linearity, sometimes jointly with constant variance, is routinely assumed in the context of sufficient dimension reduction. It is well understood that, when these conditions do not hold, blindly using them may lead to inconsistency in estimating the central subspace and the central mean subspace. Surprisingly, we discover that even if these conditions do hold, using them will bring efficiency loss. This paradoxical phenomenon is illustrated through sliced inverse regression and principal Hessian directions. The efficiency loss also applies to other dimension reduction procedures. We explain this empirical discovery by theoretical investigation. Copyright 2013, Oxford University Press.

Suggested Citation

  • Yanyuan Ma & Liping Zhu, 2013. "Efficiency loss and the linearity condition in dimension reduction," Biometrika, Biometrika Trust, vol. 100(2), pages 371-383.
    • Handle: RePEc:oup:biomet:v:100:y:2013:i:2:p:371-383
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/biomet/ass075
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

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

    Citations

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


    Cited by:

    1. Feng, Zhenghui & Wang, Tao & Zhu, Lixing, 2014. "Transformation-based estimation," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 186-205.
    2. 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.
    3. Fan, Guo-Liang & Xu, Hong-Xia & Liang, Han-Ying, 2019. "Dimension reduction estimation for central mean subspace with missing multivariate response," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    4. Wang, Qihua & Su, Miaomiao & Wang, Ruoyu, 2021. "A beyond multiple robust approach for missing response problem," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    5. 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.
    6. Zhang, Yaowu & Zhou, Yeqing & Zhu, Liping, 2024. "A post-screening diagnostic study for ultrahigh dimensional data," Journal of Econometrics, Elsevier, vol. 239(2).

    More about this item

    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:oup:biomet:v:100:y:2013:i:2:p:371-383. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/biomet .

    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.