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December 2008 Covariance regularization by thresholding
Peter J. Bickel, Elizaveta Levina
Ann. Statist. 36(6): 2577-2604 (December 2008). DOI: 10.1214/08-AOS600

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.

Citation

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Peter J. Bickel. Elizaveta Levina. "Covariance regularization by thresholding." Ann. Statist. 36 (6) 2577 - 2604, December 2008. https://doi.org/10.1214/08-AOS600

Information

Published: December 2008
First available in Project Euclid: 5 January 2009

zbMATH: 1196.62062
MathSciNet: MR2387969
Digital Object Identifier: 10.1214/08-AOS600

Subjects:
Primary: 62H12
Secondary: 62F12, 62G09

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.36 • No. 6 • December 2008
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