# Robust Semiparametric Efficient Estimators in Complex Elliptically Symmetric Distributions

**Stefano Fortunati**(IPSA, Paris, France)

October 02, 2020 — 11:00 — Online

###### Abstract

Covariance matrices play a major role in statistics, signal processing and machine learning applications. This seminar focuses on the semiparametric covariance/scatter matrix estimation problem in elliptical distributions. The class of elliptical distributions can be seen as a semiparametric model where the finite-dimensional vector of interest is given by the location vector and by the (vectorized) covariance/scatter matrix, while the density generator represents an infinite-dimensional nuisance function. The main aim of the statistical inference in elliptically distributed data is then to provide possible estimators of the finite-dimensional parameter vector able to reconcile the two dichotomic concepts of robustness and (semiparametric) efficiency. An R-estimator satisfying these requirements has been recently proposed by Hallin, Oja, and Paindaveine for real-valued elliptical data by exploiting the Le Cam’s theory of one-step efficient estimators and the rank-based statistics. In this seminar, we firstly recall the building blocks underlying the derivation of such real-valued R-estimator, then its extension to complex-valued data is proposed. Moreover, through numerical simulations, its estimation performance and robustness to outliers are investigated in a finite-sample regime. https://ieeexplore.ieee.org/document/9174925

###### Biography

Stefano FORTUNATI graduated cum laude in telecommunication engineering and received the PhD at the University of Pisa, Italy, in 2008 and 2012 respectively. In 2012, he joined the Department of “Ingegneria dell’Informazione” of the University of Pisa, where he worked as researcher with a Post-Doc position until Sept. 2019. Since Oct. 2019, he is with the Laboratoire des Signaux et Systèmes (L2S) CentraleSupélec, Gif-sur-Yvette, France. From Sept. 2020 he is a permanent lecturer (enseignant-chercheur) at IPSA in the Parisian campus of Ivry-sur-Seine. From Sept. 2012 to Nov. 2012 and from Sept. 2013 to Nov. 2013, he was a visiting researcher at the CMRE NATO Research Center in La Spezia, Italy. From May 2017 to April 2018, he spent a period of one year as visiting researcher with the Signal Processing Group, at the Technische Universität Darmstadt. He was a recipient of the 2019 EURASIP JASP Best Paper Award. Dr. Fortunati’s professional expertise encompasses different areas of the statistical signal processing, with particular focus on point estimation and hypothesis testing, performance bounds, misspecification theory, robust and semiparametric statistics and statistical learning theory.