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Marčenko–Pastur law for Tyler’s M-estimator

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  • Zhang, Teng
  • Cheng, Xiuyuan
  • Singer, Amit

Abstract

This paper studies the limiting behavior of Tyler’s M-estimator for the scatter matrix, in the regime that the number of samples n and their dimension p both go to infinity, and p/n converges to a constant y with 0

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:149:y:2016:i:c:p:114-123
    DOI: 10.1016/j.jmva.2016.03.010
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    References listed on IDEAS

    as
    1. Couillet, Romain & Kammoun, Abla & Pascal, Frédéric, 2016. "Second order statistics of robust estimators of scatter. Application to GLRT detection for elliptical signals," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 249-274.
    2. Couillet, Romain & Pascal, Frédéric & Silverstein, Jack W., 2015. "The random matrix regime of Maronna’s M-estimator with elliptically distributed samples," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 56-78.
    3. Frahm, Gabriel & Jaekel, Uwe, 2007. "Tyler's M-estimator, random matrix theory, and generalized elliptical distributions with applications to finance," Discussion Papers in Econometrics and Statistics 2/07, University of Cologne, Institute of Econometrics and Statistics.
    4. Frahm, Gabriel & Glombek, Konstantin, 2012. "Semicircle law of Tyler’s M-estimator for scatter," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 959-964.
    5. Couillet, Romain, 2015. "Robust spiked random matrices and a robust G-MUSIC estimator," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 139-161.
    Full references (including those not matched with items on IDEAS)

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