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COVARIANCE REGULARIZATION BY THRESHOLDING
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DOI：10.1214/08-AOS600.png)
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摘要
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This paper considers regularizing a covariance matrix of p variables estimated from it observations, by hard thresholding. We show that the thresholded estimate is consistent in the operator norm as long as the true covariance matrix is sparse in a suitable sense, the variables are Gaussian or sub-Gaussian, and (log p)/n -> 0, and obtain explicit rates. The results are uniform over families of covariance matrices which satisfy a fairly natural notion of sparsity. We discuss an intuitive resampling scheme for threshold selection and prove a general cross-validation result that justifies this approach. We also compare thresholding to other covariance estimators in simulations and on an example from climate data.
Keyword:
Covariance estimation
regularization
sparsity
thresholding
large p small n
high dimension low sample size
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3.7
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2.8K
被引数:
2.9W
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