# Semiparametric inference in elliptical distributions - lower bounds and efficient estimators.

**Stefano Fortunati**(L2S, CentraleSupélec)

January 31, 2020 — 11:00 — "Salle des séminaires du L2S, C4.01"

###### Abstract

A prerequisite for any statistical inference method is the notion of statistical model, i.e. a collection of probability density functions (pdfs) that is able to characterize random phenomena based on their observations. The most widely used models in signal processing applications are the parametric ones. However, parametric models are generally too “narrow” and not able to take into account the lack of a-priori information that affects inference problems in practice.

In this talk, we introduce the more general semiparametric characterization of the collected data. A semiparametric model is a set of pdfs characterized by a finite-dimensional parameter vector of interest along with an infinite-dimensional nuisance parameter, i.e. a function. We show how to obtain the Semiparametric Cramér-Rao

Bound (SCRB) for the estimation of the finite-dimensional parameter vector in the presence of nuisance functions. Furthermore, we investigate the possibility to derive estimators of the finite-dimensional parameter vector able to reconcile two dichotomic concepts: robustness and (semiparametric) efficiency.

Throughout the talk, as common thread and example to clarify the theoretical findings, inference problems in Elliptically Symmetric (ES) distributed data will be analysed. Particular attention will be devoted to the well-known covariance/scatter matrix estimation problem in the presence of an unknown density generator.

###### Biography

Stefano Fortunati graduated 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 a post-doc researcher at the Laboratoire des Signaux et Systèmes (L2S) CentraleSupélec, Gif-sur-Yvette, France. 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 is in the organizing committee of the 2020 IEEE Radar Conference to be held in Florence in September 2020. He was in the organizing committee of the 2nd Workshop on Cognitive Information Processing (CIP2010), of the 2014 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP2014) and he was the Publication Chair of the 3rd International Workshop on Compressed Sensing Theory and its Applications to Radar, Sonar and Remote Sensing (CoSeRa 2015). Dr. Fortunati’s professional expertise encompasses different areas of the statistical signal processing: estimation and detection theory, misspecification and semiparametric theory, robust statistics and performance bounds.