Open Access
November, 1981 Estimation of the Mean of a Multivariate Normal Distribution
Charles M. Stein
Ann. Statist. 9(6): 1135-1151 (November, 1981). DOI: 10.1214/aos/1176345632


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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Charles M. Stein. "Estimation of the Mean of a Multivariate Normal Distribution." Ann. Statist. 9 (6) 1135 - 1151, November, 1981.


Published: November, 1981
First available in Project Euclid: 12 April 2007

zbMATH: 0476.62035
MathSciNet: MR630098
Digital Object Identifier: 10.1214/aos/1176345632

Primary: 62F15
Secondary: 62F10 , 62F25

Keywords: Bayes estimate , confidence region , James-Stein estimate , Minimax estimate , moving average , multivariate normal mean , simultaneous estimation , trimmed mean

Rights: Copyright © 1981 Institute of Mathematical Statistics

Vol.9 • No. 6 • November, 1981
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