The Annals of Statistics
- Ann. Statist.
- Volume 36, Number 6 (2008), 2553-2576.
A CLT for regularized sample covariance matrices
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.
Ann. Statist., Volume 36, Number 6 (2008), 2553-2576.
First available in Project Euclid: 5 January 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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