IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v91y2004i2p199-223.html
   My bibliography  Save this article

Improvement of approximations for the distributions of multinomial goodness-of-fit statistics under nonlocal alternatives

Author

Listed:
  • Sekiya, Yuri
  • Taneichi, Nobuhiro

Abstract

Cressie and Read (J. Roy. Statist. Soc. B 46 (1984) 440-464) introduced the power divergence statistics, Ra, as multinomial goodness-of-fit statistics. Each Ra has a limiting noncentral chi-square distribution under a local alternative and has a limiting normal distribution under a nonlocal alternative. Taneichi et al. (J. Multivariate Anal. 81 (2002) 335-359) derived an asymptotic approximation for the distribution of Ra under local alternatives. In this paper, using multivariate Edgeworth expansion for a continuous distribution, we show how the approximation based on the limiting normal distribution of Ra under nonlocal alternatives can be improved. We apply the expansion to the power approximation for Ra. The results of numerical investigation show that the proposed power approximation is very effective for the likelihood ratio test.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:jmvana:v:91:y:2004:i:2:p:199-223
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(03)00130-1
    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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.

    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, 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.

    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:91:y:2004:i:2:p:199-223. 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.