The Annals of Statistics

Estimation of the Mean of a Multivariate Normal Distribution

Charles M. Stein

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Abstract

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.

Article information

Source
Ann. Statist. Volume 9, Number 6 (1981), 1135-1151.

Dates
First available: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176345632

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aos/1176345632

Mathematical Reviews number (MathSciNet)
MR630098

Zentralblatt MATH identifier
0476.62035

Subjects
Primary: 62F15: Bayesian inference
Secondary: 62F10: Point estimation 62F25: Tolerance and confidence regions

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

Citation

Stein, Charles M. Estimation of the Mean of a Multivariate Normal Distribution. The Annals of Statistics 9 (1981), no. 6, 1135--1151. doi:10.1214/aos/1176345632. http://projecteuclid.org/euclid.aos/1176345632.


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