Generalized Bayes minimax estimators of the mean of multivariate normal distribution with unknown variance |
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| Authors: | Martin T. Wells Gongfu Zhou |
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| Affiliation: | aCornell University, Department of Statistical Science, 301 Malott Hall Hall, Ithaca, NY 14853, USA;bYale University, Department of Epidemiology and Public Health, New Haven, CT 06520, USA |
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| Abstract: | We construct a broad class of generalized Bayes minimax estimators of the mean of a multivariate normal distribution with covariance equal to σ2Ip, with σ2 unknown, and under the invariant loss  δ(X)−θ2/σ2. Examples that illustrate the theory are given. Most notably it is shown that a hierarchical version of the multivariate Student-t prior yields a Bayes minimax estimate. |
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| Keywords: | primary, 62C20, 62C15, 62C10 secondary, 62A15 |
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