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April, 1970 A Family of Minimax Estimators of the Mean of a Multivariate Normal Distribution
A. J. Baranchik
Ann. Math. Statist. 41(2): 642-645 (April, 1970). DOI: 10.1214/aoms/1177697104


A family of estimators, each of which dominates the "usual" one, is given for the problem of simultaneously estimating means of three or more independent normal random variables which have a common unknown variance. Charles Stein [4] established the existence of such estimators (for the case of a known variance) and later, with James [3], exhibited some, both for the case of unknown common variances considered here and for other cases as well. Alam and Thompson [1] have also obtained estimators which dominate the usual one. The class of estimators given in this paper contains those of James and Stein and also those of Alam and Thompson.


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A. J. Baranchik. "A Family of Minimax Estimators of the Mean of a Multivariate Normal Distribution." Ann. Math. Statist. 41 (2) 642 - 645, April, 1970.


Published: April, 1970
First available in Project Euclid: 27 April 2007

zbMATH: 0204.52504
MathSciNet: MR253461
Digital Object Identifier: 10.1214/aoms/1177697104

Rights: Copyright © 1970 Institute of Mathematical Statistics


Vol.41 • No. 2 • April, 1970
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