IDEAS home Printed from
   My bibliography  Save this article

Semicircle law of Tyler’s M-estimator for scatter


  • Frahm, Gabriel
  • Glombek, Konstantin


This paper analyzes the spectral properties of Tyler’s M-estimator for scatter Tn,d. It is shown that if a multivariate sample stems from a generalized spherically distributed population and the sample size n and the dimension d both go to infinity while d/n→0, then the empirical spectral distribution of n/d(Tn,d−Id), Id being the identity, converges in probability to the semicircle law. In contrast to that of the sample covariance matrix, this convergence does not necessarily require the sample vectors to be componentwise independent. Further, moments of the generalized spherical population do not have to exist.

Suggested Citation

  • Frahm, Gabriel & Glombek, Konstantin, 2012. "Semicircle law of Tyler’s M-estimator for scatter," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 959-964.
  • Handle: RePEc:eee:stapro:v:82:y:2012:i:5:p:959-964
    DOI: 10.1016/j.spl.2012.01.017

    Download full text from publisher

    File URL:
    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

    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. Frahm, Gabriel & Jaekel, Uwe, 2009. "A generalization of Tyler's M-estimators to the case of incomplete data," Discussion Papers in Econometrics and Statistics 3/07, University of Cologne, Institute of Econometrics and Statistics.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. Zhang, Teng & Cheng, Xiuyuan & Singer, Amit, 2016. "Marčenko–Pastur law for Tyler’s M-estimator," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 114-123.


    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:stapro:v:82:y:2012:i:5:p:959-964. 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: (Dana Niculescu). General contact details of provider: .

    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 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.

    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.