Computational Statistics

, Volume 32, Issue 4, pp 1481–1513 | Cite as

Multivariate moment based extreme value index estimators

  • Matias Heikkilä
  • Yves Dominicy
  • Pauliina Ilmonen
Original Paper


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.


Elliptical distribution Moment estimator Mixed moment estimator 



Matias Heikkil acknowledges financial support from the Magnus Ehrnrooth foundation. Yves Dominicy acknowledges financial support via a Mandat de Chargé de Recherches FNRS. The authors wish to thank the anonymous referees for their insightful comments that helped to improve the article greatly.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Mathematics and Systems AnalysisAalto University School of ScienceEspooFinland
  2. 2.Solvay Brussels School of Economics and Management, ECARESUniversité libre de BruxellesBrusselsBelgium

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