Abstract: This paper considers comparison of MINQUE and simple estimator of Σ in the multivariate normal linear model Y~N(XB, Σ×V) under the risk of entropy loss function and symmetry loss function criterion, where the design matrix X need not have full rank and the dispersion matrix V can be singular. It is interested to prove that MINQUE is superior to simple estimator under Entropy loss function.

Key words: MINQUE, risk function, entropy loss function, symmetry loss function, multivariate linear model, MINQUE, risk function, entropy loss function, symmetry loss function