IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb475/200043.html
   My bibliography  Save this paper

Minimax optimal designs for nonparametric regression - a further optimality property of the uniform distribution

Author

Listed:
  • Biedermann, Stefanie
  • Dette, Holger

Abstract

In the common nonparametric regression model y(i) = g(ti) + a (ti) ei , i=1….,n with i.i.d - noise and nonrepeatable design points ti we consider the problem of choosing an optimal design for the estimation of the regression function g. A minimax approach is adopted which searches for designs minimizing the maximum of the asymptotic integrated mean squared error_ where the maximum is taken over an appropriately bounded class of functions (g,a). The minimax designs are found explicitly and for certain special cases the optimality of the uniform distribution can be established.

Suggested Citation

  • Biedermann, Stefanie & Dette, Holger, 2000. "Minimax optimal designs for nonparametric regression - a further optimality property of the uniform distribution," Technical Reports 2000,43, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200043
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/77122/2/2000-43.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Müller, Hans-Georg, 1984. "Optimal designs for nonparametric kernel regression," Statistics & Probability Letters, Elsevier, vol. 2(5), pages 285-290, October.
    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. Greenwood, Allen G. & Rees, Loren Paul & Siochi, Fernando C., 1998. "An investigation of the behavior of simulation response surfaces," European Journal of Operational Research, Elsevier, vol. 110(2), pages 282-313, October.

    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:zbw:sfb475:200043. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/isdorde.html .

    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.