The Annals of Statistics

Multivariate Empirical Bayes and Estimation of Covariance Matrices

Bradley Efron and Carl Morris

Full-text: Open access

Abstract

The problem of estimating several normal mean vectors in an empirical Bayes situation is considered. In this case, it reduces to the problem of estimating the inverse of a covariance matrix in the standard multivariate normal situation using a particular loss function. Estimators which dominate any constant multiple of the inverse sample covariance matrix are presented. These estimators work by shrinking the sample eigenvalues toward a central value, in much the same way as the James-Stein estimator for a mean vector shrinks the maximum likelihood estimators toward a common value. These covariance estimators then lead to a class of multivariate estimators of the mean, each of which dominates the maximum likelihood estimator.

Article information

Source
Ann. Statist., Volume 4, Number 1 (1976), 22-32.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343345

Digital Object Identifier
doi:10.1214/aos/1176343345

Mathematical Reviews number (MathSciNet)
MR394960

Zentralblatt MATH identifier
0322.62041

JSTOR
links.jstor.org

Subjects
Primary: 62F10: Point estimation
Secondary: 62C99: None of the above, but in this section

Keywords
Multivariate empirical Bayes Stein's estimator minimax estimation mean of a multivariate normal distribution estimating a covariance matrix James-Stein estimator simultaneous estimation combining estimates

Citation

Efron, Bradley; Morris, Carl. Multivariate Empirical Bayes and Estimation of Covariance Matrices. Ann. Statist. 4 (1976), no. 1, 22--32. doi:10.1214/aos/1176343345. https://projecteuclid.org/euclid.aos/1176343345


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