Dear All,

We have the pleasure thanks to the support of the ESSEC IDS dpt, Institut des Actuaires, Fondation des Sciences de la Modélisation (CY), the group Risques AEF (SFdS), to invite you to the seminar by:

Spatial quantiles (sometimes called geometric quantiles) are among the most successful concepts of multivariate quantiles. In this talk, we present some recent results on these quantiles and on their extensions. First, we discuss natural M-extensions of these quantiles, that provide in particular a spatial concept of expectiles. Second, we investigate the robustness of spatial quantiles, in terms of their finite-sample breakdown point. Last, while spatial quantiles have been limited so far to flat spaces, we present an extension of this concept to distributions on the sphere or hyperspheres; this provides in particular a new concept of depth in directional statistics, which finds natural applications in high-dimensional supervised classification.