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

摘要

The problem of estimating the mean vector μ of a multivariate normal distribution with the covariance matrix ~(σ2) _(I p) 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 etal. (2011).