IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v96y2005i1p1-19.html
   My bibliography  Save this article

L1-norm error bounds for asymptotic expansions of multivariate scale mixtures and their applications to Hotelling's generalized

Author

Listed:
  • Fujikoshi, Y.
  • Ulyanov, V.V.
  • Shimizu, R.

Abstract

This paper is concerned with the distribution of a multivariate scale mixture variate X=(X1,...,Xp)' with Xi=SiZi, where Z1,...,Zp are i.i.d. random variables, Si>0(i=1,...,p), and {S1,...,Sp} is independent of {Z1,...,Zp}. First we obtain L1-norm error bounds for an asymptotic expansion of the density function of X in the multivariate case as well as in the univariate case. Then the results are applied in obtaining error bounds for asymptotic expansions of the null distribution of Hotelling's generalized -statistic. The special features of our results are that our error bounds are given in explicit and computable forms. Further, their orders are the same as ones of the usual order estimates, and hence the paper provides a new proof for validity of the asymptotic expansions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:96:y:2005:i:1:p:1-19
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(04)00174-5
    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. Hall, Peter, 1979. "On measures of the distance of a mixture from its parent distribution," Stochastic Processes and their Applications, Elsevier, vol. 8(3), pages 357-365, May.
    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. 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.
    2. 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.
    3. 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.
    4. 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.

    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. 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.
    3. 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.

    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:96:y:2005:i:1:p:1-19. 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.