Robust shrinkage estimators of the location parameter for elliptically symmetric distributions

The estimation of the location parameter of a spherically symmetric distribution was greatly improved by Berger and Brandwein. But the authors conditions on the shrinkage estimators depend upon the complete knowledge, up to the location parameter, of the distribution of the observations. We give sufficient conditions for uniform domination of the least squares estimator relatively to a class of elliptically symmetric distributions and a family of quadratic loss functions: our results can be applied to the particular case of estimation of a normal mean vector.