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¯ + e where matrix e is distributed as elliptically contoured with unknown scale matrix §. In present work, we con- sider the problem of estimating § with respect to squared loss function, L(^§;§) = tr( ^§§?1?I)2. It is shown that improvement of the estimators were obtained by James, Stein [7], Dey and Sri- vasan [1] under the normality assumption remains robust under an elliptically contoured distribution respect to squared loss function.