Inadmissibility of the Best Fully Equivariant Estimator of the Generalized Residual Variance

Abstract

The estimation of the generalized residual variance is considered when an observable Wishart random matrix is available. It is shown that when the loss function is normalized squared error, the natural fully equivariant estimator is dominated by an alternative. The latter uses either one of two estimators depending on the result of a preliminary test of significance. This alternate estimator has an everywhere smaller mean normalized squared error than the natural estimator.