A comparison of some estimators of the variance covariance matrix when the population mean is known

Abstract

In this article, we consider the problem of estimation of variance covariance matrix a normally distributed population, when the population mean is known. We, specifically consider the maximum likelihood estimators derived under the known as well as unknown mean assumptions and test their relative merits under various loss functions. Definite results are obtained under entropy as well as squared error loss functions. Finally some open problems in this area are suggested.

Keywords:

• Admissibility
• loss function
• maximum likelihood estimator
• normal distribution