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A generalization of Tyler's M-estimators to the case of incomplete data


  • Frahm, Gabriel
  • Jaekel, Uwe


Many different robust estimation approaches for the covariance or shape matrix of multivariate data have been established until today. Tyler's M-estimator has been recognized as the 'most robust' M-estimator for the shape matrix of elliptically symmetric distributed data. Tyler's Mestimators for location and shape are generalized by taking account of incomplete data. It is shown that the shape matrix estimator remains distribution-free under the class of generalized elliptical distributions. Its asymptotic distribution is also derived and a fast algorithm, which works well even for high-dimensional data, is presented. A simulation study with clean and contaminated data covers the complete-data as well as the incomplete-data case, where the missing data are assumed to be MCAR, MAR, and NMAR.

Suggested Citation

  • 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.
  • Handle: RePEc:zbw:ucdpse:307

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    Cited by:

    1. Frahm, Gabriel & Glombek, Konstantin, 2012. "Semicircle law of Tyler’s M-estimator for scatter," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 959-964.

    More about this item


    covariance matrix; distribution-free estimation; missing data; robust estimation; shape matrix; sign-based estimator; Tyler's M-estimator;

    JEL classification:

    • H12 - Public Economics - - Structure and Scope of Government - - - Crisis Management
    • H20 - Public Economics - - Taxation, Subsidies, and Revenue - - - General


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