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


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.


Download Citation

Peter J. Bickel. Elizaveta Levina. "Covariance regularization by thresholding." Ann. Statist. 36 (6) 2577 - 2604, December 2008.


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

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

Primary: 62H12
Secondary: 62F12 , 62G09

Keywords: Covariance estimation , high dimension low sample size , large p small n , regularization , Sparsity , thresholding

Rights: Copyright © 2008 Institute of Mathematical Statistics


Vol.36 • No. 6 • December 2008
Back to Top