Estimation of scale matrix of elliptically contoured matrix distributions

In this paper, the problem of estimation of scale matrix is considered under entropy loss, quadratic loss and squared error loss. With respect to entropy and quadratic loss, we obtain the best estimator of [Sigma] having the form [alpha]Sx as well as having the form Tx[Delta]Tx', where Sx, Tx and [Delta] are given in the text, and obtain the minimax estimator of [Sigma] and the best equivariant estimator of [Sigma] with respect to the triangular transformations group. With respect to the squared error loss, we generalize the result of Dey and Srinivasan (1992).