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From Multivariate Quantiles to Copulas and Statistical Depth, and Back
The Working Group on Risk - CREAR, with the support of the IDS dpt , Institut des Actuaires, LabEx MME-DII and the group BFA-SFdS, has the pleasure to invite you to the seminar by:
Prof. Marc HALLIN, ECARES and Department of Mathematics, Université libre de Bruxelles, Belgium
“From Multivariate Quantiles to Copulas and Statistical Depth, and Back”
Wednesday November, 09 2022 12:30 to 1:30 pm (CET)
Dual format:
ESSEC Paris La Défense (CNIT), Room 237, and via Zoom, please click here
Topics:
The univariate concept of quantile function---the inverse of a distribution function---plays a fundamental role in Probability and Statistics. In dimensions two and higher, however, inverting traditional distribution functions does not lead to any satisfactory notion. In their quest for the Grail of an adequate definition, statisticians developed two extremely fruitful theoretical pathways: copula transforms, where marginal quantiles are privileged over global ones, and depth functions, where a center-outward ordering is substituting the more traditional South-West/North-East one. We show how a recent center-outward redefinition, based on measure transportation ideas, of the concept of distribution function reconciles and fine-tunes these two approaches, and eventually yields a notion of multivariate quantile matching, in arbitrary dimension d, all the properties that make univariate quantiles a successful and vital tool of statistical inference.
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Mercredi 9 novembre 2022
12h30
- 13h30
(GMT +1)
L'événement est organisé en présentiel et en ligne
ESSEC Paris La Défense (CNIT)
2 Pl. de la Défense
92800
Puteaux
En ligne
Dr. Marc Hallin is an Emeritus Professor of the Université libre de Bruxelles, where he obtained his PhD in Mathematics and has been teaching Statistics and Mathematical Statistics at the Departments of Mathematics and Economics. He also held invited positions in Lille 1, Paris 6, the Université Catholique de Louvain, and Princeton University. Author of about 240 research papers, he received several awards, among which the Senior Gottfried Noether Award of the American Statistical Association, the Pierre-Simon de Laplace Award of the Société française de Statistique, a Humboldt-Forschungspreis of the Alexander-von-Humboldt Foundation, and the Medal of the Faculty of Mathematics and Physics of Charles University in Prague. He also was the 2017 recipient of the Hermann Otto Hirschfeld Lecture Series at the Humboldt-Universität zu Berlin, the 2018 Mahalanobis Memorial Lecture at the Indian Statistical Institute, and the holder of a Catedra de Excelencia at the Universidad Carlos III de Madrid. A Fellow of the Institute of Mathematical Statistics and the American Statistical Association, he is a member of the Classe des Sciences of the Royal Academy of Belgium.
ESSEC Paris La Défense (CNIT)
2 Pl. de la Défense92800 Puteaux
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