COVARIANCE REGULARIZATION BY THRESHOLDING

• 成果类型: Article
• 署名作者: Bickel, Peter J.; Levina, Elizaveta
• 署名单位: University of California System; University of California Berkeley; University of Michigan System; University of Michigan
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/08-AOS600
• 发表日期: 2008
• 页码: 2577-2604
• 关键词: largest eigenvalue; selection; matrices; BAYES

摘要

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.