The DOI matches its Crossref record; 5 of the 5 references it cites were found in a registry or an index.
Positive-Definite ℓ1-Penalized Estimation of Large Covariance Matrices
Abstract
The thresholding covariance estimator has nice asymptotic properties for estimating sparse large covariance matrices, but it often has negative eigenvalues when used in real data analysis. To fix this drawback of thresholding estimation, we develop a positive-definite ℓ1-penalized covariance estimator for estimating sparse large covariance matrices. We derive an efficient alternating direction method to solve the challenging optimization problem and establish its convergence properties. Under weak regularity conditions, nonasymptotic statistical theory is also established for the proposed estimator. The competitive finite-sample performance of our proposal is demonstrated by both simulation and real applications.
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Subramanian, A., Tamayo, P., Mootha, V. K., Mukherjee, S., Ebert, B. L., Gillette, M. A., Paulovich, A., Pomeroy, S. L., Golub, T. R., Lander, E. S., et al. (2005) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0506580102 · Cited by 53,625
Boyd, S., Parikh, N., Chu, E., Peleato, B., & Eckstein, J. (2011) · Foundations and Trends® in Machine Learning · doi:10.1561/2200000016 · Cited by 17,075
The adaptive lasso and its oracle properties
Zou, H. (2006) · Journal of the American Statistical Association · doi:10.1198/016214506000000735 · Cited by 7,470
Self-citationKhan, J., Wei, J. S., Ringnér, M., Saal, L. H., Ladanyi, M., Westermann, F., Berthold, F., Schwab, M., Antonescu, C. R., Peterson, C., et al. (2001) · Nature Medicine · doi:10.1038/89044 · Cited by 2,644
Gene-expression profiles predict survival of patients with lung adenocarcinoma
Beer, D. G., Kardia, S. L. R., Huang, C.-C., Giordano, T. J., Levin, A. M., Misek, D. E., Lin, L., Chen, G., Gharib, T. G., Thomas, D. G., et al. (2002) · Nature Medicine · doi:10.1038/nm733 · Cited by 2,025
Cited by
Large Covariance Estimation by Thresholding Principal Orthogonal Complements
Fan, J., Liao, Y., & Mincheva, M. (2013) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/rssb.12016 · Cited by 909
Metadata
- Authors
- Xue, L., Ma, S., & Zou, H.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 2012-09-12
- Volume
- 107
- Issue
- 500
- Pages
- 1480-1491
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2113968881
- Cited by
- 159
- References
- 5
- FWCI
- 10.49
- Type
- journal article
- Language
- en
- Open access
- closed
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- Xue, L., Ma, S., & Zou, H. (2012). Positive-Definite ℓ1-Penalized Estimation of Large Covariance Matrices. Journal of the American Statistical Association. https://doi.org/10.1080/01621459.2012.725386
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