TY - JOUR
T1 - Marčenko-Pastur law for Tyler's M-estimator
AU - Zhang, Teng
AU - Cheng, Xiuyuan
AU - Singer, Amit
N1 - Funding Information:
A. Singer was partially supported by Award Number FA9550-12-1-0317 and FA9550-13-1-0076 from AFOSR , by Award Number R01GM090200 from the NIGMS , and by Award Number LTR DTD 06-05-2012 from the Simons Foundation .
Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2016/7/1
Y1 - 2016/7/1
N2 - 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 01, . . ., xn are identically and independently generated from the Gaussian distribution N(0,I), the operator norm of the difference between a properly scaled Tyler's M-estimator and ∑i=1nxixi⊤/n tends to zero. As a result, the spectral distribution of Tyler's M-estimator converges weakly to the Marčenko-Pastur distribution.
AB - 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 01, . . ., xn are identically and independently generated from the Gaussian distribution N(0,I), the operator norm of the difference between a properly scaled Tyler's M-estimator and ∑i=1nxixi⊤/n tends to zero. As a result, the spectral distribution of Tyler's M-estimator converges weakly to the Marčenko-Pastur distribution.
KW - Covariance estimation
KW - Random matrix theory
KW - Robust statistics
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U2 - 10.1016/j.jmva.2016.03.010
DO - 10.1016/j.jmva.2016.03.010
M3 - Article
AN - SCOPUS:84966378352
SN - 0047-259X
VL - 149
SP - 114
EP - 123
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
ER -