IDEAS home Printed from https://ideas.repec.org/a/taf/gnstxx/v30y2018i3p774-795.html
   My bibliography  Save this article

Asymptotic normality for plug-in estimators of diversity indices on countable alphabets

Author

Listed:
  • Michael Grabchak
  • Zhiyi Zhang

Abstract

The plug-in estimator is one of the most popular approaches to the estimation of diversity indices. In this paper, we study its asymptotic distribution for a large class of diversity indices on countable alphabets. In particular, we give conditions for the plug-in estimator to be asymptotically normal, and in the case of uniform distributions, where asymptotic normality fails, we give conditions for the asymptotic distribution to be chi-squared. Our results cover some of the most commonly used indices, including Simpson's index, Reńyi's entropy and Shannon's entropy.

Suggested Citation

  • Michael Grabchak & Zhiyi Zhang, 2018. "Asymptotic normality for plug-in estimators of diversity indices on countable alphabets," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 30(3), pages 774-795, July.
    • Handle: RePEc:taf:gnstxx:v:30:y:2018:i:3:p:774-795
    DOI: 10.1080/10485252.2018.1482294
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/10485252.2018.1482294
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/10485252.2018.1482294?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.

    More about this item

    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:taf:gnstxx:v:30:y:2018:i:3:p:774-795. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/GNST20 .

    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.