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.
Original language | English (US) |
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Pages (from-to) | 2553-2576 |
Number of pages | 24 |
Journal | Annals of Statistics |
Volume | 36 |
Issue number | 6 |
DOIs | |
State | Published - Dec 2008 |
Keywords
- Random matrices
- Regularization
- Sample covariance