This paper derives an extended version of the Haff or, more appropriately, Stein-Haff identity for an elliptically contoured distribution (ECD) . This identity is then used to show that the minimax estimators of the covariance matrix obtained under normal models remain robust under the ECD model.
"Robust improvement in estimation of a covariance matrix in an elliptically contoured distribution." Ann. Statist. 27 (2) 600 - 609, April 1999. https://doi.org/10.1214/aos/1018031209