IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v6y1976i3p369-391.html
   My bibliography  Save this article

Asymptotic expansions for distributions of latent roots in multivariate analysis

Author

Listed:
  • Constantine, A. G.
  • Muirhead, R. J.

Abstract

Asymptotic expansions are given for the distributions of latent roots of matrices in three multivariate situations. The distribution of the roots of the matrix S1(S1 + S2)-1, where S1 is Wm(n1, [Sigma], [Omega]) and S2 is Wm(n2, [Sigma]), is studied in detail and asymptotic series for the distribution are obtained which are valid for some or all of the roots of the noncentrality matrix [Omega] large. These expansions are obtained using partial-differential equations satisfied by the distribution. Asymptotic series are also obtained for the distributions of the roots of n-1S, where S in Wm(n, [Sigma]), for large n, and S1S2-1, where S1 is Wm(n1, [Sigma]) and S2 is Wm(n2, [Sigma]), for large n1 + n2.

Suggested Citation

  • Constantine, A. G. & Muirhead, R. J., 1976. "Asymptotic expansions for distributions of latent roots in multivariate analysis," Journal of Multivariate Analysis, Elsevier, vol. 6(3), pages 369-391, September.
    • Handle: RePEc:eee:jmvana:v:6:y:1976:i:3:p:369-391
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0047-259X(76)90046-4
    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.

    Citations

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


    Cited by:

    1. Chao, John C. & Phillips, Peter C. B., 2002. "Jeffreys prior analysis of the simultaneous equations model in the case with n+1 endogenous variables," Journal of Econometrics, Elsevier, vol. 111(2), pages 251-283, December.
    2. Chikuse, Yasuko, 1998. "Density Estimation on the Stiefel Manifold," Journal of Multivariate Analysis, Elsevier, vol. 66(2), pages 188-206, August.
    3. Phillips, Peter C B, 1994. "Some Exact Distribution Theory for Maximum Likelihood Estimators of Cointegrating Coefficients in Error Correction Models," Econometrica, Econometric Society, vol. 62(1), pages 73-93, January.
    4. Grant H. Hillier, 1987. "Joint Distribution Theory for Some Statistics Based on LIML and TSLS," Cowles Foundation Discussion Papers 840, Cowles Foundation for Research in Economics, Yale University.
    5. Peter D. Hoff, 2009. "A hierarchical eigenmodel for pooled covariance estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 971-992, November.
    6. Chikuse, Yasuko, 2003. "Concentrated matrix Langevin distributions," Journal of Multivariate Analysis, Elsevier, vol. 85(2), pages 375-394, 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:jmvana:v:6:y:1976:i:3:p:369-391. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.