Bayes minimax estimators of a multivariate normal mean

Tze Fen Li and Dinesh S. Bhoj

Statistics & Probability Letters, 1991, vol. 11, issue 5, 373-377

Abstract: Let X have a p-dimensional normal distribution with mean vector [theta] and identity covariance matrix I. In a compound decision problem consisting of squared error estimation of [theta] based on X, a prior distribution [Lambda] is placed on a normal class of priors to produce a family of Bayes estimators t. Let g(w) be the density of the prior distribution [Lambda]. If wg'(w)/g(w) does not change sign and is bounded, t is minimax. This condition is different from the condition obtained by Faith (1978), where wg'(w)/g(w) is nonincreasing. Based on this condition, we obtain several new families of minimax Bayes estimators.

Keywords: Admissible; Bayes; estimation; compound; decision; problem; minimax (search for similar items in EconPapers)
Date: 1991
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