Flexible multivariate Hill estimators

Yves Dominicy, Matias Heikkilä, Pauliina Ilmonen, David Veredas*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)


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 h 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.

Original languageEnglish
Publication statusE-pub ahead of print - 1 Jan 2019
MoE publication typeA1 Journal article-refereed


  • Extreme value
  • Hill estimator
  • Homogeneous function
  • Multivariate regular variation
  • Tail index

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