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December 2008 A CLT for regularized sample covariance matrices
Greg W. Anderson, Ofer Zeitouni
Ann. Statist. 36(6): 2553-2576 (December 2008). DOI: 10.1214/07-AOS503

Abstract

We consider the spectral properties of a class of regularized estimators of (large) empirical covariance matrices corresponding to stationary (but not necessarily Gaussian) sequences, obtained by banding. We prove a law of large numbers (similar to that proved in the Gaussian case by Bickel and Levina), which implies that the spectrum of a banded empirical covariance matrix is an efficient estimator. Our main result is a central limit theorem in the same regime, which to our knowledge is new, even in the Gaussian setup.

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Greg W. Anderson. Ofer Zeitouni. "A CLT for regularized sample covariance matrices." Ann. Statist. 36 (6) 2553 - 2576, December 2008. https://doi.org/10.1214/07-AOS503

Information

Published: December 2008
First available in Project Euclid: 5 January 2009

zbMATH: 1360.60047
MathSciNet: MR2485007
Digital Object Identifier: 10.1214/07-AOS503

Subjects:
Primary: 62H12
Secondary: 15A52

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.36 • No. 6 • December 2008
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