IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v97y2006i1p231-245.html
   My bibliography  Save this article

Adaptation under probabilistic error for estimating linear functionals

Author

Listed:
  • Tony Cai, T.
  • Low, Mark G.

Abstract

The problem of estimating linear functionals based on Gaussian observations is considered. Probabilistic error is used as a measure of accuracy and attention is focused on the construction of adaptive estimators which are simultaneously near optimal under probabilistic error over a collection of convex parameter spaces. In contrast to mean squared error it is shown that fully rate optimal adaptive estimators can be constructed for probabilistic error. A general construction of such estimators is provided and examples are given to illustrate the general theory.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:1:p:231-245
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(05)00029-1
    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. Efromovich, Sam, 1994. "On adaptive estimation of nonlinear functionals," Statistics & Probability Letters, Elsevier, vol. 19(1), pages 57-63, January.
    2. Low, Mark G. & Kang, Yung-Gyung, 2002. "Estimating monotone functions," Statistics & Probability Letters, Elsevier, vol. 56(4), pages 361-367, February.
    Full references (including those not matched with items on IDEAS)

    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. 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:jmvana:v:97:y:2006:i:1:p:231-245. 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.