Multivariate moment based extreme value index estimators

Matias Heikkilä*, Yves Dominicy, Pauliina Ilmonen

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review


Modeling extreme events is of paramount importance in various areas of science—biostatistics, climatology, finance, geology, and telecommunications, to name a few. Most of these application areas involve multivariate data. Estimation of the extreme value index plays a crucial role in modeling rare events. There is an affine invariant multivariate generalization of the well known Hill estimator—the separating Hill estimator. However, the Hill estimator is only suitable for heavy tailed distributions. As in the case of the separating multivariate Hill estimator, we consider estimation of the extreme value index under the assumptions of multivariate ellipticity and independent identically distributed observations. We provide affine invariant multivariate generalizations of the moment estimator and the mixed moment estimator. These estimators are suitable for both light and heavy tailed distributions. Asymptotic properties of the new extreme value index estimators are derived under multivariate elliptical distribution with known location and scatter. The effect of replacing true location and scatter by estimates is examined in a thorough simulation study. We also consider two data examples: one financial application and one meteorological application.

Original languageEnglish
Pages (from-to)1481–1513
Number of pages33
JournalComputational Statistics
Issue number4
Publication statusPublished - Dec 2016
MoE publication typeA1 Journal article-refereed


  • Elliptical distribution
  • Mixed moment estimator
  • Moment estimator


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