On the construction of Bayes minimax estimators
Dominique Fourdrinier, William E. Strawderman, Martin T. Wells
The Annals of Statistics · 1998 · Volume 26 · Issue 2
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.
Keywords
62A15, 62C10, 62C15, 62C20, Bayes estimate, minimaxity, multivariate normal mean, proper Bayes, quadratic loss, superharmonic functions
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