Regularized estimation of large covariance matrices
| dc.creator | Bickel, Peter J. | |
| dc.creator | Levina, Elizaveta | |
| dc.date | 2008-03-13 | |
| dc.date.accessioned | 2026-07-07T12:17:37Z | |
| dc.date.available | 2026-07-07T12:17:37Z | |
| dc.description | This paper considers estimating a covariance matrix of $p$ variables from $n$ observations by either banding or tapering the sample covariance matrix, or estimating a banded version of the inverse of the covariance. We show that these estimates are consistent in the operator norm as long as $(\log p)/n\to0$, and obtain explicit rates. The results are uniform over some fairly natural well-conditioned families of covariance matrices. We also introduce an analogue of the Gaussian white noise model and show that if the population covariance is embeddable in that model and well-conditioned, then the banded approximations produce consistent estimates of the eigenvalues and associated eigenvectors of the covariance matrix. The results can be extended to smooth versions of banding and to non-Gaussian distributions with sufficiently short tails. A resampling approach is proposed for choosing the banding parameter in practice. This approach is illustrated numerically on both simulated and real data. | |
| dc.description | Published in at http://dx.doi.org/10.1214/009053607000000758 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/0803.1909 | |
| dc.identifier | http://arxiv.org/abs/0803.1909 | |
| dc.identifier | Annals of Statistics 2008, Vol. 36, No. 1, 199-227 | |
| dc.identifier | doi:10.1214/009053607000000758 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/212134 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62H12 (Primary) 62F12, 62G09 (Secondary) | |
| dc.title | Regularized estimation of large covariance matrices | |
| dc.type | text |