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July, 1978 Risk Estimate Optimality of James-Stein Estimators
Terry Moore, Richard J. Brook
Ann. Statist. 6(4): 917-919 (July, 1978). DOI: 10.1214/aos/1176344265


This note extends a result of Efron and Morris on domination of the maximum likelihood estimator for the mean of a multivariate normal distribution. We show that this result and our extension follow from a certain differential inequality. In a certain class of estimators having a unique unbiased estimator for the quadratic risk we find necessary and sufficient conditions for risk estimate dominance of a particular set of estimators. We show that, in the sense of risk estimates, these conditions imply that there are no estimators in this class which dominate the James-Stein or truncated James-Stein estimators.


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Terry Moore. Richard J. Brook. "Risk Estimate Optimality of James-Stein Estimators." Ann. Statist. 6 (4) 917 - 919, July, 1978.


Published: July, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0378.62027
MathSciNet: MR478448
Digital Object Identifier: 10.1214/aos/1176344265

Primary: 62F10
Secondary: 62C99

Keywords: James-Stein estimator , mean of a multivariate normal distribution , risk estimate dominance , truncated James-Stein estimator , unbiased estimator of the risk

Rights: Copyright © 1978 Institute of Mathematical Statistics


Vol.6 • No. 4 • July, 1978
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