IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v60y2004i2p137-153.html
   My bibliography  Save this article

Minimal efficiency of designs under the class of orthogonally invariant information criteria

Author

Listed:
  • Radoslav Harman

Abstract

Consider the linear regression model with uncorrelated errors and an experimental design ξ. In the article, we address the problem of calculating the minimal efficiency of ξ with respect to the class [InlineMediaObject not available: see fulltext.] of orthogonally invariant information criteria, containing all Kiefer’s criteria of ϕ p -optimality, among others. We show that the [InlineMediaObject not available: see fulltext.]-minimal efficiency of ξ is equal to the minimal efficiency of ξ with respect to a finite class of criteria which generalize the criterion of E-optimality. We also formulate conditions under which a design is maximin efficient, i.e. the most efficiency-stable for criteria from [InlineMediaObject not available: see fulltext.]. To illustrate the results, we calculated the [InlineMediaObject not available: see fulltext.]-minimal efficiency of ϕ p (in particular D, A and E) optimal designs for polynomial regression on [−1,1] up to degree 4. Moreover, for the quadratic model we explicitly constructed the [InlineMediaObject not available: see fulltext.]-maximin efficient design. Copyright Springer-Verlag 2004

Suggested Citation

  • Radoslav Harman, 2004. "Minimal efficiency of designs under the class of orthogonally invariant information criteria," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 60(2), pages 137-153, September.
    • Handle: RePEc:spr:metrik:v:60:y:2004:i:2:p:137-153
    DOI: 10.1007/s001840300301
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s001840300301
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s001840300301?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
    ---><---

    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. Lenka Filová & Mária Trnovská & Radoslav Harman, 2012. "Computing maximin efficient experimental designs using the methods of semidefinite programming," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(5), pages 709-719, July.
    2. Samuel Rosa, 2018. "Optimal designs for treatment comparisons represented by graphs," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(4), pages 479-503, October.
    3. Katarína Burclová & Andrej Pázman, 2016. "Optimal design of experiments via linear programming," Statistical Papers, Springer, vol. 57(4), pages 893-910, December.
    4. Samuel Rosa & Radoslav Harman, 2016. "Optimal approximate designs for estimating treatment contrasts resistant to nuisance effects," Statistical Papers, Springer, vol. 57(4), pages 1077-1106, December.

    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:spr:metrik:v:60:y:2004:i:2:p:137-153. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.