Title: Flexible multivariate Hill estimators
Authors: David Veredas - Vlerick Business School (Belgium) [presenting]
Yves Dominicy - Universite libre de Bruxelles (Belgium)
Matias Heikkila - Aalto University School of Science (Finland)
Abstract: A multivariate family of Hill estimators was recently proposed for elliptically distributed random vectors. We show that the family can be generalized to a broader class and, more importantly, that ellipticity is not required. Only multivariate regular variation is needed. This flexibility in terms of both the estimator and the underlying distribution is possible because regular variation of a random vector is preserved under well-behaved homogeneous functions and, as a corollary, we obtain consistency of the new class of estimators. A Monte Carlo study is conducted to asses the finite sample properties of our estimators under different asymmetric and heavy tailed distributions.