The DOI matches its Crossref record; 30 of the 30 references it cites were found in a registry or an index.
Covariance regularization by thresholding
Open accessAbstract
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.
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Cites
Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
Fan, J., & Li, R. (2001) · Journal of the American Statistical Association · doi:10.1198/016214501753382273 · Cited by 8,900
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Sparse inverse covariance estimation with the graphical lasso
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Sparse Principal Component Analysis
Zou, H., Hastie, T., & Tibshirani, R. (2006) · Journal of Computational and Graphical Statistics · doi:10.1198/106186006x113430 · Cited by 3,152
A well-conditioned estimator for large-dimensional covariance matrices
Ledoit, O., & Wolf, M. (2004) · Journal of Multivariate Analysis · doi:10.1016/s0047-259x(03)00096-4 · Cited by 3,046
On the distribution of the largest eigenvalue in principal components analysis
Johnstone, I. M. (2001) · The Annals of Statistics · doi:10.1214/aos/1009210544 · Cited by 1,949
A Distribution-Free Theory of Nonparametric Regression
Györfi, L., Kohler, M., Krzyżak, A., & Walk, H. (2002) · Springer Series in Statistics · doi:10.1007/b97848 · Cited by 1,738
DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES
Marčenko, V. A., & Pastur, L. A. (1967) · Mathematics of the USSR-Sbornik · doi:10.1070/sm1967v001n04abeh001994 · Cited by 1,713
Model selection and estimation in the Gaussian graphical model
Yuan, M., & Lin, Y. (2007) · Biometrika · doi:10.1093/biomet/asm018 · Cited by 1,627
Regularized estimation of large covariance matrices
Bickel, P. J., & Levina, E. (2008) · The Annals of Statistics · doi:10.1214/009053607000000758 · Cited by 934
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Metadata
- Authors
- Bickel, P. J., & Levina, E.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2008-12-01
- Volume
- 36
- Issue
- 6
- Pages
- 2577-2604
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2098056745
- Cited by
- 893
- References
- 30
- FWCI
- 16.45
- Type
- journal article
- Language
- en
- Open access
- bronze
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
