IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v2y1972i1p127-134.html
   My bibliography  Save this article

On the choice of flattening constants for estimating multinomial probabilities

Author

Listed:
  • Fienberg, Stephen E.
  • Holland, Paul W.

Abstract

Bayesian estimation of the cell probabilities for the multinomial distribution (under a symmetric Dirichlet prior) leads to the use of a flattening constant [alpha] to smooth the raw cell proportions. The unsmoothed estimator corresponds to [alpha] = 0. The risk functions (under quadratic loss) of the Bayesian estimators for [alpha] > 0 are compared to that for [alpha] = 0 and this leads to an interpretation of any given choice of [alpha] > 0 in terms of the maximum number of "small" cell probabilities for which the corresponding smoothed estimator has smaller risk than the unsmoothed estimator. A real set of data is used to illustrate our interpretation of three a priori and three empirically determined choices of [alpha] that have appeared in the literature.

Suggested Citation

  • Fienberg, Stephen E. & Holland, Paul W., 1972. "On the choice of flattening constants for estimating multinomial probabilities," Journal of Multivariate Analysis, Elsevier, vol. 2(1), pages 127-134, March.
  • Handle: RePEc:eee:jmvana:v:2:y:1972:i:1:p:127-134
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0047-259X(72)90014-0
    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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Donata Marasini & Sonia Migliorati, 2006. "Combining Information from Several Groups in Estimating Characteristics of Immigrant People," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(1), pages 107-127, May.
    2. Benjamin R. Shear & Sean F. Reardon, 2021. "Using Pooled Heteroskedastic Ordered Probit Models to Improve Small-Sample Estimates of Latent Test Score Distributions," Journal of Educational and Behavioral Statistics, , vol. 46(1), pages 3-33, February.
    3. J. R. Lockwood & Katherine E. Castellano & Benjamin R. Shear, 2018. "Flexible Bayesian Models for Inferences From Coarsened, Group-Level Achievement Data," Journal of Educational and Behavioral Statistics, , vol. 43(6), pages 663-692, December.
    4. Donata Marasini & Sonia Migliorati, 2006. "Combining Information from Several Groups in Estimating Characteristics of Immigrant People," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(1), pages 107-127, May.

    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:jmvana:v:2:y:1972:i:1:p:127-134. 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.