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Estimation of a Covariance Matrix under Stein's Loss
Open accessAbstract
Stein's general technique for improving upon the best invariant unbiased and minimax estimators of the normal covariance matrix is described. The technique is to obtain solutions to a certain differential inequality involving the eigenvalues of the sample covariance matrix. Several improved estimators are obtained by solving the differential inequality. These estimators shrink or expand the sample eigenvalues depending on their magnitude. A scale invariant, adaptive minimax estimator is also obtained.
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Cited by
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Ledoit, O., & Wolf, M. (2004) · Journal of Multivariate Analysis · doi:10.1016/s0047-259x(03)00096-4 · Cited by 3,046
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Bickel, P. J., & Levina, E. (2008) · The Annals of Statistics · doi:10.1214/08-aos600 · Cited by 893
Yardibi, T., Li, J., Stoica, P., Xue, M., & Baggeroer, A. B. (2010) · IEEE Transactions on Aerospace and Electronic Systems · doi:10.1109/taes.2010.5417172 · Cited by 699
Shrinkage Algorithms for MMSE Covariance Estimation
Chen, Y., Wiesel, A., Eldar, Y. C., & Hero, A. O. (2010) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2010.2053029 · Cited by 567
Sparse permutation invariant covariance estimation
Rothman, A. J., Bickel, P. J., Levina, E., & Zhu, J. (2008) · Electronic Journal of Statistics · doi:10.1214/08-ejs176 · Cited by 560
Metadata
- Authors
- Dey, D. K., & Srinivasan, C.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1985-12-01
- Volume
- 13
- Issue
- 4
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2071346966
- Cited by
- 253
- References
- 0
- FWCI
- 4.49
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Dey, D. K., & Srinivasan, C. (1985). Estimation of a Covariance Matrix under Stein's Loss. The Annals of Statistics. https://doi.org/10.1214/aos/1176349756
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