Properties of a new R-estimator of shape matrices

This paper aims at presenting a simulative analysis of the main properties of a new R-estimator of shape matrices in Complex Elliptically Symmetric (CES) distributed observations. First proposed by Hallin, Oja and Paindaveine for the real-valued case and then extended to the complex field in our recent work, this R-estimator has the remarkable property to be, at the same time, distributionally robust and semiparametric efficient. Here, the efficiency of different possible configurations of this R-estimator are investigated by comparing the resulting Mean Square Error (MSE) with the Constrained Semiparametric Cramér-Rao Bound (CSCRB). Moreover, its robustness to outliers is assessed and compared with the one of the celebrated Tyler's estimator.