Joint Estimation of Location and Scatter in Complex Elliptically Symmetric Distributions

The joint estimation of the location vector and shape matrix a set independent identically Complex Elliptically Symmetric (CES) distributed observations is investigated from both theoretical computational viewpoints. This problem framed in original context semiparametric models allowing us to handle (generally unknown) density generator as an infinite-dimensional nuisance parameter. In first part paper, computationally efficient memory saving implementation robust semiparmaetric R-estimator for matrices derived. Building upon this result, second part, estimator, relying on Tyler’s M-estimator matrix, proposed its Mean Squared Error (MSE) performance compared with Semiparametric Cramér-Rao Bound (SCRB).