The admissible minimax estimator in Gauss–Markov model under a balanced loss function

In this paper, we investigate the admissible minimax estimator (AME) of regression coefficient in Gauss–Markov model under a balanced loss function. In the class of homogeneous linear estimators, we obtain the AME under two occasions, respectively. We also prove that the AME is a shrinkage estimator of the best linear unbiased estimator (BLUE). Furthermore, we prove that the AME dominates the BLUE under certain conditions.