An Estimator of Normal Covariance Matrix

Abstract

Abstract

Solliah (1964), by considering the group of lower triangular matrices, suggested an estimator of the normal covariance matrix Σ when the mean vector is known and the loss function is tr ${({\Sigma }^{-}{}^1\stackrel{\wedge }{\Sigma }-I)}^2$ His estimator besides being minimax is better than the MLB of Σ. In this paper, we improve upon his estimator and calculate the reduction in the risk when Σ is 2×2.