Estimation and experiments comparison with respect to the matrix risk Original Research Article

Given matrices A1, A2, B1, B2, and symmetric D a necessary and sufficient condition is established for the Löwner partial ordering (A1M+B1)(A1M+B1)′not precedes, equalsL(A2M+B2)(A2M+B2)′+D to hold for all matrices M. This result is then applied to solve statistical problems of admissible linear estimation and experiments comparison under the general multivariate linear model when one of two kinds of a matrix risk function is adopted as the criterion.