IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v97y2006i9p1941-1957.html
   My bibliography  Save this article

Error bounds for asymptotic expansions of Wilks' lambda distribution

Author

Listed:
  • Fujikoshi, Yasunori
  • Ulyanov, Vladimir V.

Abstract

Let [Lambda]=Se/Se+Sh, where Sh and Se are independently distributed as Wishart distributions Wp(q,[Sigma]) and Wp(n,[Sigma]), respectively. Then [Lambda] has Wilks' lambda distribution [Lambda]p,q,n which appears as the distributions of various multivariate likelihood ratio tests. This paper is concerned with theoretical accuracy for asymptotic expansions of the distribution of T=-nlog[Lambda]. We derive error bounds for the approximations. It is necessary to underline that our error bounds are given in explicit and computable forms.

Suggested Citation

  • Fujikoshi, Yasunori & Ulyanov, Vladimir V., 2006. "Error bounds for asymptotic expansions of Wilks' lambda distribution," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 1941-1957, October.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:9:p:1941-1957
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(06)00078-9
    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. Fujikoshi, Y. & Ulyanov, V.V. & Shimizu, R., 2005. "L1-norm error bounds for asymptotic expansions of multivariate scale mixtures and their applications to Hotelling's generalized," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 1-19, September.
    2. Ryoichi Shimizu & Yasunori Fujikoshi, 1997. "Sharp Error Bounds for Asymptotic Expansions of the Distribution Functions for Scale Mixtures," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(2), pages 285-297, June.
    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. Pham-Gia, T., 2008. "Exact distribution of the generalized Wilks's statistic and applications," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1698-1716, September.

    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. Fujikoshi, Yasunori, 2000. "Error Bounds for Asymptotic Approximations of the Linear Discriminant Function When the Sample Sizes and Dimensionality are Large," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 1-17, April.
    2. Fujikoshi, Y. & Ulyanov, V.V. & Shimizu, R., 2005. "L1-norm error bounds for asymptotic expansions of multivariate scale mixtures and their applications to Hotelling's generalized," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 1-19, September.
    3. Siotani, Minoru & Wakaki, Hirofumi, 2006. "Contributions to multivariate analysis by Professor Yasunori Fujikoshi," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 1914-1926, October.
    4. Gerd Christoph & Vladimir V. Ulyanov, 2021. "Chebyshev–Edgeworth-Type Approximations for Statistics Based on Samples with Random Sizes," Mathematics, MDPI, vol. 9(7), pages 1-28, April.
    5. Gerd Christoph & Vladimir V. Ulyanov, 2023. "Second Order Chebyshev–Edgeworth-Type Approximations for Statistics Based on Random Size Samples," Mathematics, MDPI, vol. 11(8), pages 1-18, April.

    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:1941-1957. 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.