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Estimation of the Mean of a Multivariate Normal Distribution
Open accessAbstract
Estimation of the means of independent normal random variables is considered, using sum of squared errors as loss. An unbiased estimate of risk is obtained for an arbitrary estimate, and certain special classes of estimates are then discussed. The results are applied to smoothing by use of moving averages and to trimmed analogs of the James-Stein estimate. A suggestion is made for calculating approximate confidence sets for the mean vector centered at an arbitrary estimate.
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Citations
Cites
Stein's Estimation Rule and its Competitors—An Empirical Bayes Approach
Efron, B., & Morris, C. (1973) · Journal of the American Statistical Association · doi:10.1080/01621459.1973.10481350 · Cited by 981
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Efron, B., Hastie, T., Johnstone, I., & Tibshirani, R. (2004) · The Annals of Statistics · doi:10.1214/009053604000000067 · Cited by 9,357
The adaptive lasso and its oracle properties
Zou, H. (2006) · Journal of the American Statistical Association · doi:10.1198/016214506000000735 · Cited by 7,470
Generative Modeling by Estimating Gradients of the Data Distribution
Song, Y., & Ermon, S. (2019) · arXiv · doi:10.48550/arxiv.1907.05600 · Cited by 1,453
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Carvalho, C. M., Polson, N. G., & Scott, J. G. (2010) · Biometrika · doi:10.1093/biomet/asq017 · Cited by 1,381
Metadata
- Authors
- Stein, C. M.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1981-11-01
- Volume
- 9
- Issue
- 6
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2054640142
- Cited by
- 2,729
- References
- 1
- FWCI
- 17.17
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Stein, C. M. (1981). Estimation of the Mean of a Multivariate Normal Distribution. The Annals of Statistics. https://doi.org/10.1214/aos/1176345632
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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