The Annals of Statistics
- Ann. Statist.
- Volume 9, Number 6 (1981), 1135-1151.
Estimation of the Mean of a Multivariate Normal Distribution
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 in Project Euclid: 12 April 2007
Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345632
Digital Object Identifier
doi:10.1214/aos/1176345632
Mathematical Reviews number (MathSciNet)
MR630098
Zentralblatt MATH identifier
0476.62035
JSTOR
links.jstor.org
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. Ann. Statist. 9 (1981), no. 6, 1135--1151. doi:10.1214/aos/1176345632. https://projecteuclid.org/euclid.aos/1176345632
