The Annals of Statistics

A CLT for regularized sample covariance matrices

Greg W. Anderson and Ofer Zeitouni

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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.

Article information

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

Dates
First available in Project Euclid: 5 January 2009

Permanent link to this document
https://projecteuclid.org/euclid.aos/1231165179

Digital Object Identifier
doi:10.1214/07-AOS503

Mathematical Reviews number (MathSciNet)
MR2485007

Zentralblatt MATH identifier
1360.60047

Subjects
Primary: 62H12: Estimation
Secondary: 15A52

Keywords
Random matrices sample covariance regularization

Citation

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. https://projecteuclid.org/euclid.aos/1231165179


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References

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