We investigate the problem of estimating the mean vector θ of a multivariate normal distribution with covariance matrix equal to σ²Iₚ, σ² unknown, and loss \|δ - θ\|²/σ². We first find a class of minimax estimators for this problem which enlarges a class given by Baranchik. This result is then used to show that for sufficiently large sample sizes (which never need exceed 4) proper Bayes minimax estimators exist for θ if p 5.
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William E. Strawderman (1973) studied this question.