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

Let s be matrix of residual sum of square in linearmodel y = aβ+e where matrix e is distributed as elliptically contoured with unknown scale matrix ∑ in present work, we considerthe problem of estimating 1: with respect to squared lossfunction, l(∑, 1:) = ∑(e∑^- 1 - 1)2. it is shown that improvement of the estimators were obtained by james, stein [7], dey and srivasan[i]under the normality assumption remains robust under anelliptically contoured distribution respect to squared loss function