IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v19y1994i1p57-63.html
   My bibliography  Save this article

On adaptive estimation of nonlinear functionals

Author

Listed:
  • Efromovich, Sam

Abstract

The known asymptotically efficient estimates of a nonlinear functional of an unknown function are crucially depended on prior information about a smoothness of this function. We show on example of filtering that this information is not necessary at all whenever the asymptotically efficient estimation is possible, that is, when the smoothness is sufficiently large. On the other side, if no prior information about the smoothness is given then there does not exist adaptive estimator which achieves the optimal nonadaptive rates for risk convergence.

Suggested Citation

  • Efromovich, Sam, 1994. "On adaptive estimation of nonlinear functionals," Statistics & Probability Letters, Elsevier, vol. 19(1), pages 57-63, January.
    • Handle: RePEc:eee:stapro:v:19:y:1994:i:1:p:57-63
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0167-7152(94)90069-8
    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.

    Citations

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


    Cited by:

    1. Tony Cai, T. & Low, Mark G., 2006. "Adaptation under probabilistic error for estimating linear functionals," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 231-245, January.
    2. Chicken, Eric & Cai, T. Tony, 2005. "Block thresholding for density estimation: local and global adaptivity," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 76-106, July.

    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:stapro:v:19:y:1994:i:1:p:57-63. 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: 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.