Intriguing properties of extreme geometric quantiles
vendredi 30 janvier 2015, 9h30 - 10h30
A popular way to study the tail of a distribution is to consider its extreme quantiles.
While this is a standard procedure for univariate distributions, it is harder for multivariate ones,
primarily because there is no universally accepted definition of what a multivariate quantile should be.
In this talk, I shall focus on extreme geometric quantiles. I shall discuss their asymptotics, both in
direction and magnitude, when the norm of the associated index vector tends to one.
In particular, it will appear that if a random vector X has a finite covariance matrix M, then the
magnitude of its extreme geometric quantiles grows at a fixed rate and is asymptotically
characterised by M The case when X does not have a finite covariance matrix will be tackled
in a multivariate regular variation framework.Some other intriguing properties will also
be highlighted and the results will be illustrated on simulated data.
This is joint work with Gilles Stupfler (Universite Aix-Marseille)