Bayes minimax estimation of the multivariate normal mean vector under quadratic loss functions

The problem of estimating the mean vector μ of a multivariate normal distribution with the covariance matrix σ2Ip is considered under the loss function, (δ−μ)′D(δ−μ)σ2, where σ2 is unknown and D is a known positive definite diagonal matrix. A large class of Bayes minimax estimators of μ is found. This class includes classes of estimators obtained by Lin and Mousa (1982) and Zinodiny et al. (2011).