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Covariance regularization by thresholding (2007)

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by J. Bickel , Elizaveta Levina
Citations:147 - 11 self
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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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