In this paper, we study the issue of admissibility of linear estimated functions of parameters in the multivariate linear model with respect to inequality constraints under a matrix loss and a matrix balanced loss. Under the matrix loss, when the model is not constrained, the results in the class of non-homogeneous linear estimators [Xie, 1989, Chinese Sci. Bull., 1148-1149; Xie, 1993, J. Multivariate Anal., 1071-1074] showed that the admissibility under the matrix loss and the trace loss is equivalent. However, when the model is constrained by the inequality constraints, we find this equivale...
