Original Article
Multivariate Hill Estimators
Yves Dominicy,
Pauliina Ilmonen,
David Veredas,
Yves Dominicy
Solvay Brussels School of Economics and Management, Université libre de Bruxelles, ECARES, Brussels, Belgium
Search for more papers by this authorPauliina Ilmonen
Department of Mathematics and Systems Analysis, Aalto University School of Science, Espoo, Finland
Search for more papers by this authorCorresponding Author
David Veredas
Vlerick Business School and Ghent University, Gent, Belgium
Search for more papers by this authorYves Dominicy,
Pauliina Ilmonen,
David Veredas,
Yves Dominicy
Solvay Brussels School of Economics and Management, Université libre de Bruxelles, ECARES, Brussels, Belgium
Search for more papers by this authorPauliina Ilmonen
Department of Mathematics and Systems Analysis, Aalto University School of Science, Espoo, Finland
Search for more papers by this authorCorresponding Author
David Veredas
Vlerick Business School and Ghent University, Gent, Belgium
Search for more papers by this authorSummary
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 worldwide financial market indexes.
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