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Extremes

, Volume 21, Issue 4, pp 533–550 | Cite as

Extreme value estimation for discretely sampled continuous processes

  • Holger Drees
  • Laurens de Haan
  • Feridun Turkman
Article
  • 49 Downloads

Abstract

In environmental applications of extreme value statistics, the underlying stochastic process is often modeled either as a max-stable process in continuous time/space or as a process in the domain of attraction of such a max-stable process. In practice, however, the processes are typically only observed at discrete points and one has to resort to interpolation to fill in the gaps. We discuss the influence of such an interpolation on estimators of marginal parameters as well as estimators of the exponent measure. In particular, natural conditions on the fineness of the observational scheme are developed which ensure that asymptotically the interpolated estimators behave in the same way as the estimators which use fully observed continuous processes.

Keywords

Discrete and continuous sampling Interpolation Max-stable process 

AMS 2000 Subject Classifications

Primary—62G32 Secondary—62G05, 62M30 

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Notes

Acknowledgements

L. de Haan and F. Turkman have been partly funded by FCT - Fundação para a Ciência e a Tecnologia, Portugal, through the project UID/MAT/00006/2013. H. Drees has been partly supported by DFG project DR 271/6-2 within the research unit FOR 1735. We thank two anonymous referees whose constructive remarks led to an improvement of the presentation.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, SPSTUniversity of HamburgHamburgGermany
  2. 2.Department of EconomicsErasmus University RotterdamRotterdamThe Netherlands
  3. 3.Department of StatisticsUniversity of LisbonLisboaPortugal

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