IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v97y2006i9p2041-2056.html
   My bibliography  Save this article

Non-uniform bounds for short asymptotic expansions in the CLT for balls in a Hilbert space

Author

Listed:
  • Bogatyrev, S.A.
  • Götze, F.
  • Ulyanov, V.V.

Abstract

We consider short asymptotic expansions for the probability of a sum of i.i.d. random elements to hit a ball in a Hilbert space H. The error bound for the expansion is of order O(n-1). It depends on the first 12 eigenvalues of the covariance operator only. Moreover, the bound is non-uniform, i.e. the accuracy of the approximation becomes better as the distance between a boundary of the ball and the origin in H grows.

Suggested Citation

  • Bogatyrev, S.A. & Götze, F. & Ulyanov, V.V., 2006. "Non-uniform bounds for short asymptotic expansions in the CLT for balls in a Hilbert space," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 2041-2056, October.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:9:p:2041-2056
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(06)00087-X
    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.

    References listed on IDEAS

    as
    1. Taneichi, Nobuhiro & Sekiya, Yuri & Suzukawa, Akio, 2002. "Asymptotic Approximations for the Distributions of the Multinomial Goodness-of-Fit Statistics under Local Alternatives," Journal of Multivariate Analysis, Elsevier, vol. 81(2), pages 335-359, May.
    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. Taneichi, Nobuhiro & Sekiya, Yuri & Toyama, Jun, 2011. "Improved transformed deviance statistic for testing a logistic regression model," Journal of Multivariate Analysis, Elsevier, vol. 102(9), pages 1263-1279, October.
    2. Sekiya, Yuri & Taneichi, Nobuhiro, 2004. "Improvement of approximations for the distributions of multinomial goodness-of-fit statistics under nonlocal alternatives," Journal of Multivariate Analysis, Elsevier, vol. 91(2), pages 199-223, November.
    3. Taneichi, Nobuhiro & Sekiya, Yuri & Toyama, Jun, 2014. "Transformed goodness-of-fit statistics for a generalized linear model of binary data," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 311-329.
    4. Taneichi, Nobuhiro & Sekiya, Yuri & Toyama, Jun, 2019. "Transformed statistics for tests of conditional independence in J×K×L contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 193-208.
    5. Taneichi, Nobuhiro & Sekiya, Yuri, 2007. "Improved transformed statistics for the test of independence in rxs contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 98(8), pages 1630-1657, September.

    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:97:y:2006:i:9:p:2041-2056. 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/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.