Robust Improvements in Estimation of Mean and Covariance Matrices in Elliptically Contoured Distribution

This paper derives extended versions of 'Stein' and 'Haff' or more appropriately 'Stein-Haff' identities for elliptically contoured distribution (ECD) models. These identities are then used to establish the robustness of shrinkage estimators for the regression parameters in the multivariate linear regression model when the error matrix follows ECD model. Both invariant and non-invariant loss functions are considered in the above model as well as in the growth curve model. Also, the robustness of minimax estimators for the scale matrix in ECD models is established. Other results include the robustness, in a restricted ECD model, of the dominance results for the estimation of a scale with unknown locations and for the estimation of variance components in two components one-way mixed linear model with replicates.