IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4612-2856-1_73.html
   My bibliography  Save this book chapter

Stochastic Approximation in Bootstrap and Bayesian Approaches to Interval Estimation in Hierarchical Models

In: Computing Science and Statistics

Author

Listed:
  • Jeffrey A. Longmate

    (University of Florida, Department of Statistics)

Abstract

The empirical Bayes approach to shrinkage estimation does not extend easily to interval estimation because it neglects error in the prior. One method of obtaining valid intervals is to calibrate them to provide the desired coverage in bootstrap samples. A stochastic approximation algorithm is proposed that accomplishes the necessary integration by nesting an easy numerical integration inside a Monte Carlo integration. Examining sensitivity to the specification of the bootstrap distribution leads naturally to a Bayesian approach, via the assumption of a (hyper) prior over a family of bootstrap distributions. If the posterior distribution is intractable, the imputation-posterior algorithm of Tanner and Wong can be used. The use of a (hyper) prior obviates the need for an ad-hoc calibration parameter, and allows computation of intervals for population parameters as well as individuals.

Suggested Citation

  • Jeffrey A. Longmate, 1992. "Stochastic Approximation in Bootstrap and Bayesian Approaches to Interval Estimation in Hierarchical Models," Springer Books, in: Connie Page & Raoul LePage (ed.), Computing Science and Statistics, pages 446-450, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2856-1_73
    DOI: 10.1007/978-1-4612-2856-1_73
    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:978-1-4612-2856-1_73. 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.