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...

Pickands coordinates were introduced as a crucial tool for the investigation of bivariate extreme value models. We extend their definition to arbitrary dimensions and, thus, we can generalize many known results for bivariate extreme value and generalized Pareto models to higher dimensions and...

Let (U,V) be a random vector with U[less-than-or-equals, slant]0, V[less-than-or-equals, slant]0. The random variables Z=V/(U+V), C=U+V are the Pickands coordinates of (U,V). They are a useful tool for the investigation of the tail behavior in bivariate peaks-over-threshold models in extreme...

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....

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.

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...

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

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...

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...