IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-211-49905-4_10.html
   My bibliography  Save this book chapter

Nonstandard likelihood ratio test in exponential families

In: The Strength of Nonstandard Analysis

Author

Listed:
  • Jacques Bosgiraud

    (Universíté Paris VIII)

Abstract

Let (p θ) θ∈Θ be an exponential family in ℝk. After establishing nonstandard results about large deviations of the sample mean $$ \overline X $$ , this paper defines the nonstandard likelihood ratio test of the null hypothesis H 0 : θ ∈ hal( $$ \widetilde\Theta _0 $$ ), where $$ \widetilde\Theta _0 $$ is a standard subset of Θ and hal( $$ \widetilde\Theta _0 $$ ) its halo. If α is the level of the test, depending on whether lnα/n is infinitesimal or not we obtain different rejection criteria. We calculate risks of the first and second kinds (external probabilities) and prove that this test is more powerful than any “regular” nonstandard test based on $$ \overline X $$ .

Suggested Citation

  • Jacques Bosgiraud, 2007. "Nonstandard likelihood ratio test in exponential families," Springer Books, in: Imme van den Berg & Vítor Neves (ed.), The Strength of Nonstandard Analysis, chapter 10, pages 145-169, Springer.
    • Handle: RePEc:spr:sprchp:978-3-211-49905-4_10
    DOI: 10.1007/978-3-211-49905-4_10
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:sprchp:978-3-211-49905-4_10. 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.