Joint Estimation of Location and Scatter in Complex Elliptically Symmetric Distributions A robust semiparametric and computationally efficient R-estimator of the shape matrix

Stefano Fortunati , Alexandre Renaux (1) , Frédéric Pascal

1 L2S - Laboratoire des signaux et systèmes

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

Keywords: Semiparametric models robust estimators efficient estimators covariance matrix Complex Elliptically Symmetric (CES) distributions; Semiparametric models; robust estimators; efficient estimators; covariance matrix; Complex Elliptically Symmetric (CES) distributions

Domains: Signal and Image processing

Stefano Fortunati, Alexandre Renaux, Frédéric Pascal. Joint Estimation of Location and Scatter in Complex Elliptically Symmetric Distributions A robust semiparametric and computationally efficient R-estimator of the shape matrix. Journal of Signal Processing Systems, 2022, 94, pp.133-146. ⟨10.1007/s11265-021-01674-y⟩. ⟨hal-03948514⟩