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A CLT FOR REGULARIZED SAMPLE COVARIANCE MATRICES
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DOI：10.1214/07-AOS503.png)
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摘要
En 中文
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.
Keyword:
Random matrices
sample covariance
regularization
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期刊
IF:
3.7
论文数:
2.8K
被引数:
2.9W
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