Marchenko-Pastur Law for Tyler ’ s and Maronna ’ s M-estimators

  title={Marchenko-Pastur Law for Tyler ’ s and Maronna ’ s M-estimators},
  author={Teng Zhang and Amit Singer},
This paper studies the limiting behavior of Tyler’s and Maronna’s Mestimators, in the regime that the number of samples n and the dimension p both go to infinity, and p/n converges to a constant y with 0 < y < 1. We prove that when the data samples are identically and independently generated from the Gaussian distribution N(0, I), the difference between the sample covariance matrix and a scaled version of Tyler’s M-estimator or Maronna’s M-estimator tends to zero in spectral norm, and the… CONTINUE READING
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