Matrix linear minimax estimators in a general multivariate linear model under a balanced loss function

This article investigates the minimaxity of matrix linear estimators of regression coefficient matrix in a general multivariate linear model with a nonnegative definite covariance matrix allowing for relations between the covariance matrix and the design matrix under a balanced loss function. In a subset of all matrix linear estimators, matrix linear minimax estimators are obtained and proved to be unique almost surely on the suitable hypotheses.