Loading...
Flexible multivariate hill estimators
Dominicy, Yves Heikkilä, Matias Ilmonen, Pauliina Veredas, David
Dominicy, Yves
Heikkilä, Matias
Ilmonen, Pauliina
Veredas, David
Citations
Altmetric:
Publication Type
Journal article with impact factor
Editor
Supervisor
Publication Year
2020
Journal
Journal of Econometrics
Book
Publication Volume
217
Publication Issue
2
Publication Begin page
398
Publication End page
410
Publication Number of pages
Collections
Abstract
Dominicy et al. (2017) introduce a family of Hill estimators for elliptically distributed and heavy tailed random vectors. They propose to use the univariate Hill to a norm of order of the data. The norms are homogeneous functions of order one. We show that the family of estimators can be generalized to homogeneous functions of any order and, more importantly, that ellipticity is not required. Only multivariate regular variation is needed, as it is preserved under well-behaved homogeneous functions. This enables us to have flexibility in terms of the estimator and the underlying distribution. Consistency and asymptotic normality are shown, and a Monte Carlo study is conducted to assess the finite sample properties under different asymmetric and heavy tailed multivariate distributions. We illustrate the estimators with an application to 10 years of daily data of paid claims from property insurance policies across 15 regions of Belgium.
Research Projects
Organizational Units
Journal Issue
Keywords
Tail Index, Hill Estimator, Extreme Value, Multivariate Regular Variation, Homogeneous Function