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 OLSEKeywords: multivariate linear model, MINQUE, BLUE, OLSE, Wishart -distribution