IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v128y2014icp1-9.html
   My bibliography  Save this article

Stochastic domination in predictive density estimation for ordered normal means under α-divergence loss

Author

Listed:
  • Chang, Yuan-Tsung
  • Strawderman, William E.

Abstract

We consider stochastic domination in predictive density estimation problems when the underlying loss metric is α-divergence, D(α), loss introduced by Csiszàr (1967). The underlying distributions considered are normal location-scale models, including the distribution of the observables, the distribution of the variable whose density is to be predicted, and the estimated predictive density which will be taken to be of the plug-in type. The scales may be known or unknown. We derive a general expression for the α-divergence loss in this set-up and show that it is a concave monotone function of quadratic loss, and also a function of the variances (predicand and plug-in). We demonstrate D(α) stochastic domination of certain plug-in predictive densities over others for the entire class of metrics simultaneously when üsual” stochastic domination holds in the related problem of estimating the mean with respect to quadratic loss. Examples of D(α) stochastic domination presented relate to the problem of estimating the predictive density of the variable with the larger mean.

Suggested Citation

  • Chang, Yuan-Tsung & Strawderman, William E., 2014. "Stochastic domination in predictive density estimation for ordered normal means under α-divergence loss," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 1-9.
    • Handle: RePEc:eee:jmvana:v:128:y:2014:i:c:p:1-9
    DOI: 10.1016/j.jmva.2014.02.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X1400044X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2014.02.014?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. Chang, Yuan-Tsung & Strawderman, William E., 2015. "A note on stochastic domination for discrete exponential families," Statistics & Probability Letters, Elsevier, vol. 98(C), pages 131-135.

    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:128:y:2014:i:c:p:1-9. 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.