Title: Tail behaviour of a multivariate quantile based on optimal transport
Authors: Cees de Valk - Université catholique de Louvain (Belgium) [presenting]
Johan Segers - Universite catholique de Louvain (Belgium)
Abstract: Recently, an attractive multivariate quantile based on Monge-Kantorovitch optimal transport was proposed as a refinement of half-space depth: a map transforming a spherical reference distribution function to the distribution function of interest is sought which minimises the mean square of the size of the displacement. We explore the use of this idea for estimation of multivariate tail quantiles. Beginning with the assumption of multivariate regular variation, we consider limit relations satisfied by the optimal map and the associated quantile. An example of an application is discussed.