IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v59y2004i3p289-303.html
   My bibliography  Save this article

A statistical treatment of the problem of division

Author

Listed:
  • C. Andy Tsao
  • Yu-Ling Tseng

Abstract

The problem of division is one of the most important problems in the emergence of probability. It has been long considered “solved” from a probabilistic viewpoint. However, we do not find the solution satisfactory. In this study, the problem is recasted as a statistical problem. The outcomes of matches of the game are considered as an infinitely exchangeable random sequence and predictors/estimators are constructed in light of de Finetti representation theorem. Bounds of the estimators are derived over wide classes of priors (mixing distributions). We find that, although conservative, the classical solutions are justifiable by our analysis while the plug-in estimates are too optimistic for the winning player. Copyright Springer-Verlag 2004

Suggested Citation

  • C. Andy Tsao & Yu-Ling Tseng, 2004. "A statistical treatment of the problem of division," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 59(3), pages 289-303, June.
    • Handle: RePEc:spr:metrik:v:59:y:2004:i:3:p:289-303
    DOI: 10.1007/s001840300285
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s001840300285
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s001840300285?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. C. Tsao & Yu-Ling Tseng, 2006. "Confidence estimation for tolerance intervals," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(3), pages 441-456, September.

    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:59:y:2004:i:3:p:289-303. 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.