The sample covariance is not efficient for elliptical distributions

it is ell known that the sample covariance is not an efficient estimator of the covariance of a bivariate normal vector, We extend this result to elliptical distributions and e propose a simple explicit estimator, which is efficient ill the normal case and which outperforms the sample covariance in general. Necessary and sufficient conditions are established under which this estimator is in general efficient for an elliptical distribution. (C) 2001 Elsevier Science.