Stein's Estimation Rule and its Competitors—An Empirical Bayes Approach
Abstract
Stein's estimator for k normal means is known to dominate the MLE if k ≥ 3. In this article we ask if Stein's estimator is any good in its own right. Our answer is yes: the positive part version of Stein's estimator is one member of a class of “good” rules that have Bayesian properties and also dominate the MLE. Other members of this class are also useful in various situations. Our approach is by means of empirical Bayes ideas. In the later sections we discuss rules for more complicated estimation problems, and conclude with results from empirical linear Bayes rules in non-normal cases.
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In empirical Bayes, factorisations of the likelihood create empirical priors that share properties of both likelihood and priors.
“In empirical Bayes [9], factorisations of the likelihood create empirical priors that share properties of both the likelihood and priors.”
From Hierarchical Models in the Brain (2008) · cites this paper as [9]
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- Authors
- Efron, B., & Morris, C.
- Affiliations
- Stanford University (US)
- RAND Corporation (US)
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1973-03
- Volume
- 68
- Issue
- 341
- Pages
- 117-130
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2072857774
- Cited by
- 981
- References
- 1
- Citations by year
- 2026: 12 · 2025: 14 · 2024: 23 · 2023: 24 · 2022: 26 · 2021: 41 · 2020: 22 · 2019: 60 · 2018: 28 · 2017: 23 · 2016: 35 · 2015: 27 · 2014: 44 · 2013: 23 · 2012: 40
- FWCI
- 14.55
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of the American Statistical Association (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Methods and Mixture Models
- Keywords
- James-Stein estimator, empirical Bayes, multivariate normal mean estimation, maximum likelihood estimator
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