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Multivariate moment based extreme value index estimators

Author

Listed:
  • Matias Heikkilä

    (Aalto University School of Science)

  • Yves Dominicy

    (Université libre de Bruxelles)

  • Pauliina Ilmonen

    (Aalto University School of Science)

Abstract

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.

Suggested Citation

  • Matias Heikkilä & Yves Dominicy & Pauliina Ilmonen, 2017. "Multivariate moment based extreme value index estimators," Computational Statistics, Springer, vol. 32(4), pages 1481-1513, December.
    • Handle: RePEc:spr:compst:v:32:y:2017:i:4:d:10.1007_s00180-016-0706-y
    DOI: 10.1007/s00180-016-0706-y
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    References listed on IDEAS

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    1. Yves Dominicy & Hiroaki Ogata & David Veredas, 2013. "Inference for vast dimensional elliptical distributions," Computational Statistics, Springer, vol. 28(4), pages 1853-1880, August.
    2. Einmahl, J. H.J. & Dekkers, A. L.M. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Other publications TiSEM 81970cb3-5b7a-4cad-9bf6-2, Tilburg University, School of Economics and Management.
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