IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v126y2016i1p118-137.html
   My bibliography  Save this article

Sharp tail distribution estimates for the supremum of a class of sums of i.i.d. random variables

Author

Listed:
  • Major, Péter

Abstract

We take a class of functions F with polynomially increasing covering numbers on a measurable space (X,X) together with a sequence of i.i.d. X-valued random variables ξ1,…,ξn, and give a good estimate on the tail behaviour of supf∈F∑j=1nf(ξj) if the relations supx∈X|f(x)|≤1, Ef(ξ1)=0 and Ef(ξ1)2<σ2 hold with some 0≤σ≤1 for all f∈F. Roughly speaking this estimate states that under some natural conditions the above supremum is not much larger than the largest element taking part in it. The proof heavily depends on the main result of paper Major (2015). We also present an example that shows that our results are sharp, and compare them with results of earlier papers.

Suggested Citation

  • Major, Péter, 2016. "Sharp tail distribution estimates for the supremum of a class of sums of i.i.d. random variables," Stochastic Processes and their Applications, Elsevier, vol. 126(1), pages 118-137.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:1:p:118-137
    DOI: 10.1016/j.spa.2015.07.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414915001969
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2015.07.017?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.

    References listed on IDEAS

    as
    1. Deheuvels, Paul & Einmahl, John H. J. & Mason, David M. & Ruymgaart, Frits H., 1988. "The almost sure behavior of maximal and minimal multivariate kn-spacings," Journal of Multivariate Analysis, Elsevier, vol. 24(1), pages 155-176, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Carando, Daniel & Fraiman, Ricardo & Groisman, Pablo, 2009. "Nonparametric likelihood based estimation for a multivariate Lipschitz density," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 981-992, May.
    2. Claire Coiffard, 2011. "On the Hausdorff dimension of exceptional random sets generated by multivariate spacings," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(3), pages 359-371, 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:spapps:v:126:y:2016:i:1:p:118-137. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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/505572/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.