The Annals of Statistics

A CLT for regularized sample covariance matrices

Greg W. Anderson and Ofer Zeitouni

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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.

Article information

Ann. Statist., Volume 36, Number 6 (2008), 2553-2576.

First available in Project Euclid: 5 January 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62H12: Estimation
Secondary: 15A52

Random matrices sample covariance regularization


Anderson, Greg W.; Zeitouni, Ofer. A CLT for regularized sample covariance matrices. Ann. Statist. 36 (2008), no. 6, 2553--2576. doi:10.1214/07-AOS503.

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