We present a new method for estimating the frontier of a multidimensional sample. The estimator is based on a kernel regression on high order moments. It is assumed that the order of the moments goes to infinity while the bandwidth of the kernel goes to zero. The consistency of the estimator is...

It is well-known that the univariate generalized Pareto distributions (GPD) are characterized by their peaks-over-threshold (POT) stability. We extend this result to multivariate GPDs. It is also shown that this POT stability is asymptotically shared by distributions which are in a certain...

In order to construct confidence sets for a marginal density f of a strictly stationary continuous time process observed over the time interval [0, T], it is necessary to have at one's disposal a Central Limit Theorem for the kernel density estimator fT. In this paper we address the question...