Multivariate Hill Estimators
Dominicy, Yves Ilmonen, Pauliina Veredas, David
Dominicy, Yves
Ilmonen, Pauliina
Veredas, David
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Publication Type
Journal article with impact factor
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Supervisor
Publication Year
2017
Journal
International Statistical Review
Book
Publication Volume
85
Publication Issue
1
Publication Begin page
108
Publication End page
142
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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 worldwide financial market indexes.
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Keywords
Accounting & Finance, Hill Estimator, Elliptical Distribution, Minimum Covariance Determinant, Tail Index, L_H norm