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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 $0<y<1$.
Distribution of eigenvalues for some sets of random matrices
V. A. Marčenko and L. A. Pastur · 1967
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A distribution-free M-estimator of multivariate scatter
D. E. Tyler · 1987
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Matrix Analysis
R. Bhatia · 1997
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On Tyler’s M-functional of scatter in high dimension
L. Dümbgen · 1998
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Local operator theory, random matrices and banach spaces
K. Davidson and S. Szarek · 2001
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Robust antenna array processing using M-estimators of pseudo-covariance
E. Ollila and V. Koivunen · 2003
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Math 710: Measure concentration
A. Barvinok · 2005
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Tyler’s M-estimator, random matrix theory, and generalized elliptical distributions with applications to finance
G. Frahm and U. Jaekel · 2007
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I. M. Johnstone · 2007
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Spectral Analysis of Large Dimensional Random Matrices
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Concentration of measure and spectra of random matrices: Applications to correlation matrices, elliptical distributions and beyond
N. El Karoui · 2009
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Robust shrinkage estimation of high-dimensional covariance matrices
Y. Chen, A. Wiesel, and A. Hero · 2011
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Semicircle law of Tyler’s M-estimator for scatter
G. Frahm and K. Glombek · 2012
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Distribution-free detection under complex elliptically symmetric clutter distribution
E. Ollila and D. Tyler · 2012
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Algorithms and hardness for robust subspace recovery
M. Hardt and A. Moitra · 2013
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Robust estimates of covariance matrices in the large dimensional regime
R. Couillet, F. Pascal, and J. Silverstein · 2014
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Large dimensional analysis of robust M-estimators of covariance with outliers
D. Morales-Jimenez, R. Couillet, and M. McKay · 2015
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Robust subspace recovery by Tyler’s M-estimator
T. Zhang · 2015
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Geodesic convexity and covariance estimation
A. Wiesel · 2012
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Second order statistics of robust estimators of scatter. application to GLRT detection for elliptical signals
R. Couillet, A. Kammoun, and F. Pascal · 2016
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