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Multivariate Hill Estimators
Author(s) -
Dominicy Yves,
Ilmonen Pauliina,
Veredas David
Publication year - 2017
Publication title -
international statistical review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.051
H-Index - 54
eISSN - 1751-5823
pISSN - 0306-7734
DOI - 10.1111/insr.12120
Subject(s) - estimator , mathematics , multivariate statistics , parametric statistics , extremum estimator , m estimator , class (philosophy) , statistics , computer science , artificial intelligence
Summary 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.