IDEAS home Printed from https://ideas.repec.org/a/taf/gnstxx/v25y2013i2p339-359.html
   My bibliography  Save this article

Higher-order expansions and efficiencies of tests based on spacings

Author

Listed:
  • Sherzod M. Mirakhmedov
  • S. Rao Jammalamadaka

Abstract

Statistics based on spacings, or the gaps between points, have been widely used in many contexts, primarily in testing goodness of fit. This paper derives Edgeworth-type asymptotic expansions for the sum of functions of s -step spacings where s , the order of spacings, may increase together with the sample size n . When s is fixed, it is known that only the Greenwood test, based on the sum of squares of these spacings, is first-order asymptotically efficient. In contrast, it is shown here that if s goes to infinity, there exist many other tests which are first-order efficient. We introduce and study the second-order efficiency of such tests and show that if s is sufficiently large relative to n , the Greenwood test is no longer second-order efficient. Interestingly, we see that the common phenomenon of first-order efficiency implying second-order efficiency does not hold true in this situation.

Suggested Citation

  • Sherzod M. Mirakhmedov & S. Rao Jammalamadaka, 2013. "Higher-order expansions and efficiencies of tests based on spacings," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(2), pages 339-359, June.
    • Handle: RePEc:taf:gnstxx:v:25:y:2013:i:2:p:339-359
    DOI: 10.1080/10485252.2012.755530
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/10485252.2012.755530
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/10485252.2012.755530?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. M. Ekström & S. M. Mirakhmedov & S. Rao Jammalamadaka, 2020. "A class of asymptotically efficient estimators based on sample spacings," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 617-636, September.

    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:25:y:2013:i:2:p:339-359. 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.