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Marcenko-Pastur law for Tyler’s M-estimator

Author(s): Zhang, Teng; Cheng, Xiuyuan; Singer, Amit

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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 pin converges to a constant y with 0 < y < 1. We prove that when the data samples, x(1), ... , x(n) are identically and independently generated from the Gaussian distribution (0, 1), the operator norm of the difference between a properly scaled Tyler’s M-estimator and Sigma(n)(i=1)xixi T/n tends to zero. As a result, the spectral distribution of Tyler’s M-estimator converges weakly to the Marcenko-Pastur distribution. (C) 2016 Elsevier Inc. All rights reserved.
Publication Date: Jul-2016
Electronic Publication Date: 12-Apr-2016
Citation: Zhang, Teng, Cheng, Xiuyuan, Singer, Amit. (2016). Marcenko-Pastur law for Tyler’s M-estimator. JOURNAL OF MULTIVARIATE ANALYSIS, 149 (114 - 123. doi:10.1016/j.jmva.2016.03.010
DOI: doi:10.1016/j.jmva.2016.03.010
ISSN: 0047-259X
Pages: 114 - 123
Type of Material: Journal Article
Version: Author's manuscript

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