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Extremes

, Volume 19, Issue 1, pp 79–103 | Cite as

Likelihood estimators for multivariate extremes

  • Raphaël HuserEmail author
  • Anthony C. Davison
  • Marc G. Genton
Article

Abstract

The main approach to inference for multivariate extremes consists in approximating the joint upper tail of the observations by a parametric family arising in the limit for extreme events. The latter may be expressed in terms of componentwise maxima, high threshold exceedances or point processes, yielding different but related asymptotic characterizations and estimators. The present paper clarifies the connections between the main likelihood estimators, and assesses their practical performance. We investigate their ability to estimate the extremal dependence structure and to predict future extremes, using exact calculations and simulation, in the case of the logistic model.

Keywords

Asymptotic relative efficiency Censored likelihood Logistic model Multivariate extremes Pairwise likelihood Point process approach 

AMS 2000 Subject Classifications

Primary 62F99 Secondary 62H12 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Raphaël Huser
    • 1
    Email author
  • Anthony C. Davison
    • 2
  • Marc G. Genton
    • 1
  1. 1.CEMSE DivisionKing Abdullah University of Science and TechnologyThuwalSaudi Arabia
  2. 2.EPFL, FSB-MATHAA-STATLausanneSwitzerland

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