On multivariate separating Hill estimator under estimated location and scatter

Matias Heikkilä*, Yves Dominicy, Pauliina Ilmonen

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We consider estimating the tail-index of a distribution under the assumption of multivariate ellipticity. Recently, a separating Hill estimator for multivariate elliptical distributions was proposed. This estimator is an affine invariant alternative to using the marginal observations in tail-index estimation and is hence unaffected by, e.g. change of units of measurement. However, the separating Hill estimator depends on the location and scatter of the elliptical distribution, which, in practice, have to be estimated. The effect of replacing the true location and scatter of the distribution by estimates has previously been only examined through simulations. In this article we show that the error caused by replacing the location and scatter of the distribution by estimates indeed is asymptotically negligible. This fact is essential for the practicality of the separating Hill estimator. In addition to providing the theoretical results, we present simulation results on the asymptotic behaviour of the estimators.

Original languageEnglish
Pages (from-to)1-20
JournalSTATISTICS
DOIs
Publication statusPublished - 20 Nov 2018
MoE publication typeA1 Journal article-refereed

Keywords

  • 62G32
  • 62H12
  • elliptical distribution
  • extreme value index
  • Multivariate extreme value theory

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