Covariance regularization by thresholding
| dc.creator | Bickel, Peter J. | |
| dc.creator | Levina, Elizaveta | |
| dc.date | 2009-01-20 | |
| dc.date.accessioned | 2026-07-07T12:32:11Z | |
| dc.date.available | 2026-07-07T12:32:11Z | |
| dc.description | 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 $(\log p)/n\to0$, 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. | |
| dc.description | Published in at http://dx.doi.org/10.1214/08-AOS600 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/0901.3079 | |
| dc.identifier | http://arxiv.org/abs/0901.3079 | |
| dc.identifier | Annals of Statistics 2008, Vol. 36, No. 6, 2577-2604 | |
| dc.identifier | doi:10.1214/08-AOS600 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/216697 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62H12 (Primary) 62F12, 62G09 (Secondary) | |
| dc.title | Covariance regularization by thresholding | |
| dc.type | text |