Matched, mismatched and semiparametric inference in elliptical distributions

L2S, Centrale Supelec, Gif-sur-Yvette

Date(s) : 08/04/2022   iCal
14 h 30 min - 15 h 30 min

Any scientific experiment, which aims to gain some knowledge about a real-word phenomenon, starts with the data collection. In statistics and signal processing, all the available knowledge about a physical phenomenon of interest is summarized in the probability density function (pdf) of the collected observations. To this end, we have to define a model, that is a family of pdfs that are able to statistically characterize the observations. The most used class of models are the parametric ones which however require the perfect match between the actual data distribution and the assumed model itself. Nevertheless, in practice, a certain amount of mismatch is often inevitable. Therefore, being aware about the possible performance loss that the derived estimator could undergone under model misspecification is of crucial importance. Even more important would be the possibility to overcome this misspecification problem. This can be achieved by adopting the more general semiparametric characterization of the statistical behavior of the collected data.

In this seminar we use theset of elliptical distribution as “fil rouge” to analyses the three above-mentionedaspects. In particular, we start with an introduction about classical parametric inference in the ellipticalmodel, with particular attention to the Maximum Likelihood (ML) estimator ofthe data covariance matrix. Then, the quantification of the performance lossdue to a wrong Gaussianity assumption on the data distribution will beaddressed. Finally, a new class of distributionally robust and semiparametric efficient R-estimatorsof the data covariance will be presented and their performance compared withthe one of the more “classical” M-estimators.

Keywords: Semiparametric inference, data mismatch, M-estimators, R-estimators.

Shortbio: Stefano FORTUNATI received the graduate degree in telecommunication engineering and the Ph.D. degree, both from the University of Pisa, Italy, in 2008 and 2012, respectively. In 2012, he joined the Department of Ingegneria del l’Informazione, University of Pisa, where he was a researcher with a postdoc position until September 2019. Since October 2019, he is an associate researcher at Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire des Signaux et Systems (L2S), 91190, 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 September 2012 to November 2012 and from September 2013 to November 2013, he was a Visiting Researcher with the CMRE NATO Research Center, La Spezia, Italy. From May 2017 to April 2018, he spent a period of one year as a Visiting Researcher with the Signal Processing Group, Technische Universität Darmstadt. His professional expertise encompasses different areas of the statistical signal processing and applied statistics, with particular focus on point estimation and hypothesis testing, performance bounds, misspecification theory, robust and semiparametric statistics and statistical learning theory.



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