Multivariate Hill Estimators. (29th October 2015)

• Record Type: Journal Article
• Authors: Dominicy, Yves; Ilmonen, Pauliina; Veredas, David
• Is Part Of: International statistical review. Volume 85:Number 1(2017)
• Page Start: 108
• Page End: 142
• Publication Date: 2015-10-29
• Subjects: Hill estimator -- elliptical distribution -- minimum covariance determinant -- tail index -- Lh norm; Statistics -- Periodicals; Statistics -- Bibliography -- Periodicals; Statistics -- Bibliography; Statistics -- Periodicals; Statistique; Statistique -- Périodiques; Statistique -- Bibliographie -- Périodiques; Statistique -- Étude et enseignement -- Périodiques; Statistique -- Étude et enseignement -- Bibliographie -- Périodiques; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519.2
• DOI: 10.1111/insr.12120
• Languages: English
• ISSNs: 0306-7734

Abstract

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.