Robust Semiparametric Joint Estimators of Location and Scatter in Elliptical Distributions

This paper focuses on the joint estimation of the location vector and the shape matrix of a set of Complex Elliptically Symmetric (CES) distributed observations. This well-known estimation problem is framed in the original context of semiparametric models allowing us to handle the (generally unknown) density generator as an \textit{infinite-dimensional} nuisance parameter. A joint estimator, relying on the Tyler's $M$-estimator of location and on a new $R$-estimator of shape matrix, is proposed and its Mean Squared Error (MSE) performance compared with the Semiparametric Cram\'{e}r-Rao Bound (CSCRB).