Estimation of the scale matrix of a class of elliptical distributions

Abstract.

The problem of estimation of the scale matrix of a class of elliptical distributions is considered. We propose an improved class of estimators for scale matrix. The exact forms of the risk functions are derived as well. The relative merits of the class of improved estimators to the usual one are appraised in the light of a quadratic loss function. The conditions under which the class of proposed estimators outperform the class of usual estimators are obtained. Relative Risk is also computed for a special case. Some important characteristics of scale matrix are also considered for estimation.