A CLT for regularized sample covariance matrices

The Annals of Statistics · 2008 · Volume 36 · Issue 6

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.

Keywords

15A52, 62H12, random matrices, regularization, Sample covariance

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