IDEAS home Printed from https://ideas.repec.org/p/eca/wpaper/2013-357401.html
   My bibliography  Save this paper

On Bounded Completeness and The L1-Densensess of Likelihood Ratios

Author

Listed:
  • Marc Hallin
  • Bas Werker
  • Bo Zhou

Abstract

The classical concept of bounded completeness and its relation to sufficiency and ancillarity play a fundamental role in unbiased estimation, unbiased testing, and the validity of inference in the presence of nuisance parameters. In this short note, we provide a direct proof of a little-known result by Farrell (1962) on a characterization of bounded completeness based on an L1 denseness property of the linear span of likelihood ratios. As an application, we show that an experiment with infinite-dimensional observation space is boundedly complete iff suitably chosen restricted subexperiments with finitedimensional observation spaces are.

Suggested Citation

  • Marc Hallin & Bas Werker & Bo Zhou, 2023. "On Bounded Completeness and The L1-Densensess of Likelihood Ratios," Working Papers ECARES 2023-07, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:eca:wpaper:2013/357401
    as

    Download full text from publisher

    File URL: https://dipot.ulb.ac.be/dspace/bitstream/2013/357401/3/2023-07-HALLIN_WERKER_ZHOU-on-bounded.pdf
    File Function: Œuvre complète ou partie de l'œuvre
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. D. Plachky & A. Rukhin, 1991. "Characterization of some types of completeness resp. Total completeness and their conservation under direct products," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 38(1), pages 369-376, December.
    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.

      More about this item

      Keywords

      sufficiency; completeness; ancillarity; Brownian motion; Mazur’s theorem;
      All these keywords.

      NEP fields

      This paper has been announced in the following NEP Reports:

      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:eca:wpaper:2013/357401. 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: Benoit Pauwels (email available below). General contact details of provider: https://edirc.repec.org/data/arulbbe.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.