Study of MINQUE and Simple estimator of Covariance Matrix in the multivariate linear Model

Abstract

      Under the multivariate linear model equality of MINQUE and so called"simple" estimator with , for Σ is considered. It is revealed that this equality holds if and only if the quadratic form  admits a Wishart-distribution under multivariate normality of Y. Also comparison of MINQUE and simple estimator of Σ in the multivariate normal linear model under the risk of entropy loss function criterion where the design matrix X need not have full rank and the dispersion matrix V can be singular A is considered . It is interested to prove that MINQUE is superior to simple estimator OLSE