IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v122y2012i2p449-465.html
   My bibliography  Save this article

The central limit theorem for sums of trimmed variables with heavy tails

Author

Listed:
  • Berkes, István
  • Horváth, Lajos

Abstract

Trimming is a standard method to decrease the effect of large sample elements in statistical procedures, used, e.g., for constructing robust estimators and tests. Trimming also provides a profound insight into the partial sum behavior of i.i.d. sequences. There is a wide and nearly complete asymptotic theory of trimming, with one remarkable gap: no satisfactory criteria for the central limit theorem for modulus trimmed sums have been found, except for symmetric random variables. In this paper we investigate this problem in the case when the variables are in the domain of attraction of a stable law. Our results show that for modulus trimmed sums the validity of the central limit theorem depends sensitively on the behavior of the tail ratio P(X>t)/P(|X|>t) of the underlying variable X as t→∞ and paradoxically, increasing the number of trimmed elements does not generally improve partial sum behavior.

Suggested Citation

  • Berkes, István & Horváth, Lajos, 2012. "The central limit theorem for sums of trimmed variables with heavy tails," Stochastic Processes and their Applications, Elsevier, vol. 122(2), pages 449-465.
  • Handle: RePEc:eee:spapps:v:122:y:2012:i:2:p:449-465
    DOI: 10.1016/j.spa.2011.10.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414911002663
    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. Lajos Horváth & Gregory Rice, 2014. "Rejoinder on: Extensions of some classical methods in change point analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 287-290, June.
    2. Bazarova, Alina & Berkes, István & Horváth, Lajos, 2014. "On the central limit theorem for modulus trimmed sums," Statistics & Probability Letters, Elsevier, vol. 86(C), pages 61-67.

    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:spapps:v:122:y:2012:i:2:p:449-465. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.