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Statistical Inference for Max-Stable Processes by Conditioning on Extreme Events

  • Sebastian Engelke (a1), Alexander Malinowski (a2), Marco Oesting (a3) and Martin Schlather (a3)

Abstract

In this paper we provide the basis for new methods of inference for max-stable processes ξ on general spaces that admit a certain incremental representation, which, in important cases, has a much simpler structure than the max-stable process itself. A corresponding peaks-over-threshold approach will incorporate all single events that are extreme in some sense and will therefore rely on a substantially larger amount of data in comparison to estimation procedures based on block maxima. Conditioning a process η in the max-domain of attraction of ξ on being extremal, several convergence results for the increments of η are proved. In a similar way, the shape functions of mixed moving maxima (M3) processes can be extracted from suitably conditioned single events η. Connecting the two approaches, transformation formulae for processes that admit both an incremental and an M3 representation are identified.

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Copyright

Corresponding author

Postal address: Université de Lausanne, UNIL-Dorigny, Bâtiment Extranef, 1015 Lausanne, Switzerland. Email address: sebastian.engelke@unil.ch
∗∗ Postal address: Institut für Mathematik, Universität Mannheim, A5, 6, 68131 Mannheim, Germany.
∗∗ Email address: malinows@math.uni-goettingen.de
∗∗∗∗ Postal address: INRA, UMR 518 Math. Info. Appli., Rue Claude Bernard, 75005 Paris, France. Email address: marco.oesting@agroparistech.fr
∗∗∗∗∗ Email address: schlather@math.uni-mannheim.de

References

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Keywords

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Statistical Inference for Max-Stable Processes by Conditioning on Extreme Events

  • Sebastian Engelke (a1), Alexander Malinowski (a2), Marco Oesting (a3) and Martin Schlather (a3)

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