IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v41y1999i3p215-227.html
   My bibliography  Save this article

Bounds for robust maximum likelihood and posterior consistency in compound mixture state experiments

Author

Listed:
  • Majumdar, Suman
  • Gilliland, Dennis
  • Hannan, James

Abstract

Uniform bounds on rates of L1-consistency for the empiric mean of state sequences in a family of probability models (compound with finite-mixture-state component) are obtained for MLEs (Section sec2) and posterior means for quasi-uniform hyperpriors (Section sec3), both determined in the iid mixture (empirical Bayes) sub-models. Qualitative aspects of results of this type were described by Robbins (1951). Application to the Gilliland and Hannan (1974/86) restricted-risk-finite-state-component compound decision problem (Section sec4) yields uniform bounds on rates of asymptotic regret of Bayes solutions therein (with extension to mixture-state by expectation), giving strong affirmation to an asymptotic form of a Robbins (1951) conjecture. The general extension to mixture-state components (Remark rem4.1) strengthens much of the existing compound literature.

Suggested Citation

  • Majumdar, Suman & Gilliland, Dennis & Hannan, James, 1999. "Bounds for robust maximum likelihood and posterior consistency in compound mixture state experiments," Statistics & Probability Letters, Elsevier, vol. 41(3), pages 215-227, February.
    • Handle: RePEc:eee:stapro:v:41:y:1999:i:3:p:215-227
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(98)00158-8
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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:eee:stapro:v:41:y:1999:i:3:p:215-227. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.