IDEAS home Printed from https://ideas.repec.org/p/zbw/ucdpse/507.html
   My bibliography  Save this paper

Asymptotic distributions of robust shape matrices and scales

Author

Listed:
  • Frahm, Gabriel

Abstract

It has been frequently observed in the literature that many multivariate statistical methods require the covariance or dispersion matrix ∑ of an elliptical distribution only up to some scaling constant. If the topic of interest is not the scale but only the shape of the elliptical distribution, it is not meaningful to focus on the asymptotic distribution of an estimator for ∑ or another matrix Γ ∝ ∑. In the present work, robust estimators for the shape matrix and the associated scale are investigated. Explicit expressions for their joint asymptotic distributions are derived. It turns out that if the joint asymptotic distribution is normal, the presented estimators are asymptotically independent for one and only one specific choice of the scale function. If it is non-normal (this holds for example if the estimators for the shape matrix and scale are based on the minimum volume ellipsoid estimator) only the presented scale function leads to asymptotically uncorrelated estimators. This is a generalization of a result obtained by Paindaveine (2008) in the context of local asymptotic normality theory.

Suggested Citation

  • Frahm, Gabriel, 2008. "Asymptotic distributions of robust shape matrices and scales," Discussion Papers in Econometrics and Statistics 5/07, University of Cologne, Institute of Econometrics and Statistics.
  • Handle: RePEc:zbw:ucdpse:507
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/44943/1/608699551.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Andrew J. Patton, 2004. "On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(1), pages 130-168.
    2. Fortin, Ines & Kuzmics, Christoph, 2002. "Tail-Dependence in Stock-Return Pairs," Economics Series 126, Institute for Advanced Studies.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    local asymptotic normality; M-estimator; R-estimator; robust covariance matrix estimator; scale-invariant function; S-estimator; shape matrix; Tyler's M-estimator;

    JEL classification:

    • H20 - Public Economics - - Taxation, Subsidies, and Revenue - - - General
    • E20 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - General (includes Measurement and Data)

    Statistics

    Access and download statistics

    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:zbw:ucdpse:507. 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: (ZBW - German National Library of Economics). General contact details of provider: http://edirc.repec.org/data/sxkoede.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.