ROBUST SEMIPARAMETRIC JOINT ESTIMATORS OF LOCATION AND SCATTER IN ELLIPTICAL DISTRIBUTIONS

Stefano Fortunati (1) , Alexandre Renaux (1) , Frédéric Pascal (1)

1 L2S - Laboratoire des signaux et systèmes

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 semipara-metric models allowing us to handle the (generally unknown) density generator as an 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 Cramér-Rao Bound (CSCRB).

Mots clés: Elliptical distribution; robust estimator; covariance estimation; semiparametric model; efficiency

Domaines: Traitement du signal et de l'image [eess.SP]; Applications [stat.AP]; Théorie [stat.TH]

Stefano Fortunati, Alexandre Renaux, Frédéric Pascal. ROBUST SEMIPARAMETRIC JOINT ESTIMATORS OF LOCATION AND SCATTER IN ELLIPTICAL DISTRIBUTIONS. 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), Sep 2020, Espoo, Finland. pp.1-6, ⟨10.1109/MLSP49062.2020.9231865⟩. ⟨hal-02976889⟩