A family of admissible minimax estimators of the mean of a multivariate,normal distribution |
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Authors: | Tze Fen Li Dinesh S. Bhoj |
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Abstract: | Let X has a p-dimensional normal distribution with mean vector θ and identity covariance matrix I. In a compound decision problem consisting of squared-error estimation of θ, Strawderman (1971) placed a Beta (α, 1) prior distribution on a normal class of priors to produce a family of Bayes minimax estimators. We propose an incomplete Gamma(α, β) prior distribution on the same normal class of priors to produce a larger family of Bayes minimax estimators. We present the results of a Monte Carlo study to demonstrate the reduced risk of our estimators in comparison with the Strawderman estimators when θ is away from the zero vector. |
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Keywords: | admissible Bayes estimation compound decision problem compound risk minimax |
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