A well-known result in extreme value theory indicates that componentwise taken sample maxima of random vectors are asymptotically independent under weak conditions. However, in important cases this independence is attained at a very slow rate so that the residual dependence structure plays a...

Classical discriminant analysis focusses on Gaussian and nonparametric models where in the second case the unknown densities are replaced by kernel densities based on the training sample. In the present article we assume that it suffices to base the classification on exceedances above higher...

It is well known that the marginal maxima of n standard normal random vectors with correlation coefficient ρ1 are asymptotically independent. In this article, the residual dependence will be captured by asymptotic expansions and certain penultimate distributions including the case where...

A short, elegant proof of an inequality concerning the approximate sufficiency of sparse order statistics is established which enables us to improve previous results.

A new approach to the asymptotic treatment of multivariate sample maxima is suggested and exemplified in the particular case of maxima of normal random vectors. In the limit one obtains a class of multivariate maxstable distributions not considered in literature so far.

This paper deals with the estimation of dependence parameters in certain bivariate generalized Pareto models which are models for exceedances (peaks) over high thresholds. A unified approach is obtained by using canonical parameters. An estimator, which is related to a best linear unbiased...

Bivariate generalized Pareto distributions (GPs) with uniform margins are introduced and elementary properties such as peaks-over-threshold (POT) stability are discussed. A unified parameterization with parameter [theta][set membership, variant][0,1] of the GPs is provided by their canonical...

This paper concerns the statistical modelling of Poisson processes. It consists of an intermediate step of replacing truncated empirical point processes by Poisson processes having identical intensity measures and, secondly, the building of models of limiting Poisson processes. The second step...

Multivariate extreme value distribution functions (EVDs) with standard reverse exponential margins and the pertaining multivariate generalized Pareto distribution functions (GPDs) can be parametrized in terms of their Pickands dependence function D with D=1 representing tail independence....