We propose two classes of semi-parametric estimators for the tail index of a regular varying elliptical random vector. The first one is based on the distance between a tail probability contour and the observations outside this contour. We denote it as the class of separating estimators. The...

Modeling and understanding multivariate extreme events is challenging, but of great importance in various applications — e.g. in biostatistics, climatology, and finance. The separating Hill estimator can be used in estimating the extreme value index of a heavy tailed multivariate elliptical...

Modeling extreme events is of paramount importance in various areas of science — biostatistics, climatology, finance, geology, and telecommunications, to name a few. Most of these application areas involve multivariate data. Estimation of the extreme value index plays a crucial role in...

Several recent papers treated robust and efficient estimation of tail index parameters for (equivalent) Pareto and truncated exponential models, for large and small samples...

Recently, new nonparametric multivariate extensions of the univariate sign methods have been proposed. Randles (2000) introduced an affine invariant multivariate sign test for the multivariate location problem. Later on, Hettmansperger and Randles (2002) considered an affine equivariant...

In the paper we present an R package MNM dedicated to multivariate data analysis based on the L_1 norm. The analysis proceeds very much as does a traditional multivariate analysis. The regular L_2 norm is just replaced by different L_1 norms, observation vectors are replaced by their...