IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v22y1987i2p230-244.html
   My bibliography  Save this article

Asymptotically optimal selection of a piecewise polynomial estimator of a regression function

Author

Listed:
  • Chen, Keh-Wei

Abstract

Let (X, Y) be a pair of random variables such that X = (X1,..., Xd) ranges over a nondegenerate compact d-dimensional interval C and Y is real-valued. Let the conditional distribution of Y given X have mean [theta](X) and satisfy an appropriate moment condition. It is assumed that the distribution of X is absolutely continuous and its density is bounded away from zero and infinity on C. Without loss of generality let C be the unit cube. Consider an estimator of [theta] having the form of a piecewise polynomial of degree kn based on mnd cubes of length 1/mn, where the mnd(dkn+d) coefficients are chosen by the method of least squares based on a random sample of size n from the distribution of (X, Y). Let (kn, mn) be chosen by the FPE procedure. It is shown that the indicated estimator has an asymptotically minimal squared error of prediction if [theta] is not of the form of piecewise polynomial.

Suggested Citation

  • Chen, Keh-Wei, 1987. "Asymptotically optimal selection of a piecewise polynomial estimator of a regression function," Journal of Multivariate Analysis, Elsevier, vol. 22(2), pages 230-244, August.
    • Handle: RePEc:eee:jmvana:v:22:y:1987:i:2:p:230-244
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0047-259X(87)90087-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.

    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:22:y:1987:i:2:p:230-244. 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.