The Annals of Statistics

On the construction of Bayes minimax estimators

Dominique Fourdrinier, William E. Strawderman, and Martin T. Wells

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Abstract

Bayes estimation of the mean of a multivariate normal distribution is considered under quadratic loss. We show that, when particular spherical priors are used, the superharmonicity of the square root of the marginal density provides a viable method for constructing (possibly proper) Bayes (and admissible) minimax estimators. Examples illustrate the theory; most notably it is shown that a multivariate Student-$t$ prior yields a proper Bayes minimax estimate.

Article information

Source
Ann. Statist., Volume 26, Number 2 (1998), 660-671.

Dates
First available in Project Euclid: 31 July 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1028144853

Digital Object Identifier
doi:10.1214/aos/1028144853

Mathematical Reviews number (MathSciNet)
MR1626063

Zentralblatt MATH identifier
0929.62004

Subjects
Primary: 62C20: Minimax procedures 62C15: Admissibility 62C10: Bayesian problems; characterization of Bayes procedures
Secondary: 62A15

Keywords
Bayes estimate minimaxity multivariate normal mean proper Bayes quadratic loss superharmonic functions

Citation

Fourdrinier, Dominique; Strawderman, William E.; Wells, Martin T. On the construction of Bayes minimax estimators. Ann. Statist. 26 (1998), no. 2, 660--671. doi:10.1214/aos/1028144853. https://projecteuclid.org/euclid.aos/1028144853


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