IDEAS home Printed from https://ideas.repec.org/a/bla/stanee/v56y2002i4p453-478.html
   My bibliography  Save this article

Adaptive estimation with soft thresholding penalties

Author

Listed:
  • Jean–Michel Loubes
  • Sara Van De Geer

Abstract

We show that various robust nonparametric regression estimators, such as the least absolute deviations estimator, can be made adaptive (up to logarithmic factors), by adding a soft thresholding type penalty to the loss function. As an example, we consider the situation where the roughness of the regression function is described by a single parameter p. The theory is complemented with a simulation study.

Suggested Citation

  • Jean–Michel Loubes & Sara Van De Geer, 2002. "Adaptive estimation with soft thresholding penalties," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 56(4), pages 453-478, November.
    • Handle: RePEc:bla:stanee:v:56:y:2002:i:4:p:453-478
    DOI: 10.1111/1467-9574.t01-1-00212
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/1467-9574.t01-1-00212
    Download Restriction: no
    File URL: https://libkey.io/10.1111/1467-9574.t01-1-00212?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
    ---><---

    Citations

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


    Cited by:

    1. Laan Mark J. van der & Dudoit Sandrine & Vaart Aad W. van der, 2006. "The cross-validated adaptive epsilon-net estimator," Statistics & Risk Modeling, De Gruyter, vol. 24(3), pages 373-395, December.
    2. Anne Vanhems & Jean-Michel Loubes, 2004. "Saturation spaces for regularization methods in inverse problems," Econometric Society 2004 North American Summer Meetings 380, Econometric Society.
    3. Jhong, Jae-Hwan & Koo, Ja-Yong, 2019. "Simultaneous estimation of quantile regression functions using B-splines and total variation penalty," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 228-244.

    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:bla:stanee:v:56:y:2002:i:4:p:453-478. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0039-0402 .

    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.