Canadian Journal of Statistics

A family of admissible minimax estimators of the mean of a multivariate, normal distribution

Journal Article

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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