Sparse permutation invariant covariance estimation
| dc.creator | Rothman, Adam J. | |
| dc.creator | Bickel, Peter J. | |
| dc.creator | Levina, Elizaveta | |
| dc.creator | Zhu, Ji | |
| dc.date | 2008-01-31 | |
| dc.date | 2008-06-26 | |
| dc.date.accessioned | 2026-07-07T09:46:31Z | |
| dc.date.available | 2026-07-07T09:46:31Z | |
| dc.description | The paper proposes a method for constructing a sparse estimator for the inverse covariance (concentration) matrix in high-dimensional settings. The estimator uses a penalized normal likelihood approach and forces sparsity by using a lasso-type penalty. We establish a rate of convergence in the Frobenius norm as both data dimension $p$ and sample size $n$ are allowed to grow, and show that the rate depends explicitly on how sparse the true concentration matrix is. We also show that a correlation-based version of the method exhibits better rates in the operator norm. We also derive a fast iterative algorithm for computing the estimator, which relies on the popular Cholesky decomposition of the inverse but produces a permutation-invariant estimator. The method is compared to other estimators on simulated data and on a real data example of tumor tissue classification using gene expression data. | |
| dc.description | Published in at http://dx.doi.org/10.1214/08-EJS176 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/0801.4837 | |
| dc.identifier | http://arxiv.org/abs/0801.4837 | |
| dc.identifier | Electronic Journal of Statistics 2008, Vol. 2, 494-515 | |
| dc.identifier | doi:10.1214/08-EJS176 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163558 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62H20 (Primary) 62H12 (Secondary) | |
| dc.title | Sparse permutation invariant covariance estimation | |
| dc.type | text |