Robust Improvement in Estimation of a Covariance Matrix in an Elliptically Contoured Distribution Respect to Quadratic Loss Function

Let S be matrix of residual sum of square in linear model Y = A beta + e where matrix e is distributed as elliptically contoured with unknown scale matrix Sigma. In present work, we consider the problem of estimating Sigma with respect to squared loss function, L((Sigma) over cap, Sigma) = tr ((Sigma) over cap, Sigma(-1) -I)(2). It is shown that improvement of the estimators were obtained by James, Stein [7], Dey and Srivasan [1] under the normality assumption remains robust under an elliptically contoured distribution respect to squared loss function.