Multivariate Hill Estimators

Abstract

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 second one is based on the norm of an arbitrary order. We denote it as the class of angular estimators. We show the asymptotic properties and the finite sample performances of both classes. We also illustrate the separating estimators with an empirical application to 21 world-wide financial market indexes.

Keywords: Hill estimator, elliptical distributions, Minimum Covariance Determinant, tail index

JEL Classification: C14, C51, G15