Semicircle Law for Tyler's M-Estimator of Scatter
Gabriel Frahm, Konstantin Glombek
TL;DR
This paper proves that the spectral distribution of Tyler's M-estimator for scatter converges in probability to the semicircle law, revealing a fundamental spectral property of this estimator.
Contribution
It establishes the convergence of Tyler's M-estimator's spectral distribution to the semicircle law, a novel theoretical result in high-dimensional statistics.
Findings
Spectral distribution converges to the semicircle law in probability.
Provides theoretical insight into the spectral behavior of Tyler's M-estimator.
Enhances understanding of robust scatter estimators in high dimensions.
Abstract
We show convergence in probability of the spectral distribution of Tyler's M-estimator for scatter to the semicircle law.
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Taxonomy
TopicsRandom Matrices and Applications · Mathematical functions and polynomials · Bayesian Methods and Mixture Models