Advanced Search
MyIDEAS: Login to save this article or follow this journal

Influence functions and efficiencies of the canonical correlation and vector estimates based on scatter and shape matrices

Contents:

Author Info

  • Taskinen, Sara
  • Croux, Christophe
  • Kankainen, Annaliisa
  • Ollila, Esa
  • Oja, Hannu
Registered author(s):

    Abstract

    In this paper, the influence functions and limiting distributions of the canonical correlations and coefficients based on affine equivariant scatter matrices are developed for elliptically symmetric distributions. General formulas for limiting variances and covariances of the canonical correlations and canonical vectors based on scatter matrices are obtained. Also the use of the so-called shape matrices in canonical analysis is investigated. The scatter and shape matrices based on the affine equivariant Sign Covariance Matrix as well as the Tyler's shape matrix serve as examples. Their finite sample and limiting efficiencies are compared to those of the Minimum Covariance Determinant estimators and S-estimator through theoretical and simulation studies. The theory is illustrated by an example.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://www.sciencedirect.com/science/article/B6WK9-4G1V67M-1/2/9773eb6e4b77e168ba1ca4dbbad0b4ae
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 97 (2006)
    Issue (Month): 2 (February)
    Pages: 359-384

    as in new window
    Handle: RePEc:eee:jmvana:v:97:y:2006:i:2:p:359-384

    Contact details of provider:
    Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description

    Order Information:
    Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
    Web: https://shop.elsevier.com/order?id=622892&ref=622892_01_ooc_1&version=01

    Related research

    Keywords: Canonical correlations Canonical variables Canonical vectors Shape matrix Sign covariance matrix Tyler's estimate;

    References

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    1. Anderson, T. W., 1999. "Asymptotic Theory for Canonical Correlation Analysis," Journal of Multivariate Analysis, Elsevier, vol. 70(1), pages 1-29, July.
    2. Croux, Christophe & Haesbroeck, Gentiane, 1999. "Influence Function and Efficiency of the Minimum Covariance Determinant Scatter Matrix Estimator," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 161-190, November.
    3. Thomas P. Hettmansperger, 2002. "A practical affine equivariant multivariate median," Biometrika, Biometrika Trust, vol. 89(4), pages 851-860, December.
    4. Eaton, M. L. & Tyler, D., 1994. "The Asymptotic Distribution of Singular-Values with Applications to Canonical Correlations and Correspondence Analysis," Journal of Multivariate Analysis, Elsevier, vol. 50(2), pages 238-264, August.
    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 in new window

    Cited by:
    1. Frahm, Gabriel, 2009. "Asymptotic distributions of robust shape matrices and scales," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1329-1337, August.
    2. Zhou, Jianhui, 2009. "Robust dimension reduction based on canonical correlation," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 195-209, January.
    3. Hallin, Marc & Paindaveine, Davy, 2009. "Optimal tests for homogeneity of covariance, scale, and shape," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 422-444, March.
    4. Taskinen, Sara & Koch, Inge & Oja, Hannu, 2012. "Robustifying principal component analysis with spatial sign vectors," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 765-774.
    5. Ella Roelant & Stefan Aelst & Gert Willems, 2009. "The minimum weighted covariance determinant estimator," Metrika, Springer, vol. 70(2), pages 177-204, September.
    6. Cator, Eric A. & LopuhaƤ, Hendrik P., 2010. "Asymptotic expansion of the minimum covariance determinant estimators," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2372-2388, November.
    7. Paindaveine, Davy, 2008. "A canonical definition of shape," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2240-2247, October.

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:97:y:2006:i:2:p:359-384. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.