Minimax Estimation of a Multivariate Normal Mean under a Quadratic Loss Function with Unknown Weights

摘要

This paper considers the minimax estimation of mu by delta relative to a certain quadratic loss function with unknown weights. To the best of our knowledge, this is the first time in the literature a loss function of this type is considered in estimating mu. The minimax estimation of mu relative to other types of quadratic loss functions has been extensively studied since Stein (1956) showed that the maximum likelihood estimator chi, is inadmissible, when p greater than or equal to 3, relative to the loss function given by a stated equation.