The Annals of Mathematical Statistics

A Family of Minimax Estimators of the Mean of a Multivariate Normal Distribution

A. J. Baranchik

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Abstract

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.

Article information

Source
Ann. Math. Statist., Volume 41, Number 2 (1970), 642-645.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177697104

Digital Object Identifier
doi:10.1214/aoms/1177697104

Mathematical Reviews number (MathSciNet)
MR253461

JSTOR
links.jstor.org

Citation

Baranchik, A. J. A Family of Minimax Estimators of the Mean of a Multivariate Normal Distribution. Ann. Math. Statist. 41 (1970), no. 2, 642--645. doi:10.1214/aoms/1177697104. https://projecteuclid.org/euclid.aoms/1177697104


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