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. © Institute of Mathematical Statistics,2008.
CITATION STYLE
Anderson, G. W., & Zeitouni, O. (2008). A CLT for regularized sample covariance matrices. Annals of Statistics, 36(6), 2553–2576. https://doi.org/10.1214/07-AOS503
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