[SFdS] Information du groupe BFA
WG Risk - 9 November 2022 - Prof. Marc HALLIN

Dear All,

We have the pleasure thanks to the support of the ESSEC IDS dpt, Institut des Actuaires, LabEx MME-DII, the group BFA (SFdS), to invite you to the seminar by:

Prof. Marc HALLIN
ECARES and Department of Mathematics
Université libre de Bruxelles, Belgium

Date: Wednesday, November 9 at 12:30 pm (Paris) and 6:30 pm (Singapore)

Dual format: ESSEC Paris La Défense (CNIT), Room 237, and via Zoom, please click here
(Password/Code : WGRisk)

« From Multivariate Quantiles to Copulas and Statistical Depth, and Back »

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.

Kind regards,
Jeremy Heng, Olga Klopp and Marie Kratz
and Riada Djebbar (Singapore Actuarial Society - ERM)

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