The Linear Admissible and Minimax Estimators in Seemingly Unrelated Regression Model under Matrix Loss

In this paper, we study the Seemingly Unrelated Regression Model with design matrices have same range space. We give the necessary and sufficient conditions that a linear estimator of regression coefficient is lenear admissible under matrix loss. The results generalize t;he conclusions got before by others. We also give a unique linear minimax estimator of regression coefficient in a regression model under matrix loss.It shows that the information of other models doesn’t play a role in estimation.