Covariance regularization by thresholding

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Covariance regularization by thresholding (2007)

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by J. Bickel , Elizaveta Levina

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147 - 11 self

BibTeX

@TECHREPORT{Bickel07covarianceregularization,
    author = {J. Bickel and Elizaveta Levina},
    title = {Covariance regularization by thresholding},
    institution = {},
    year = {2007}
}

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Abstract

This paper considers regularizing a covariance matrix of p variables estimated from n 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. 1. Introduction. Estimation

Keyphrases

covariance regularization covariance matrix natural notion climate data general cross-validation result operator norm true covariance matrix thresholded estimate covariance estimator suitable sense intuitive resampling scheme threshold selection hard thresholding explicit rate

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