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June 2014 Statistical inference for max-stable processes by conditioning on extreme events
Sebastian Engelke, Alexander Malinowski, Marco Oesting, Martin Schlather
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Adv. in Appl. Probab. 46(2): 478-495 (June 2014). DOI: 10.1239/aap/1401369703

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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Sebastian Engelke. Alexander Malinowski. Marco Oesting. Martin Schlather. "Statistical inference for max-stable processes by conditioning on extreme events." Adv. in Appl. Probab. 46 (2) 478 - 495, June 2014. https://doi.org/10.1239/aap/1401369703

Information

Published: June 2014
First available in Project Euclid: 29 May 2014

zbMATH: 1291.60106
MathSciNet: MR3215542
Digital Object Identifier: 10.1239/aap/1401369703

Subjects:
Primary: 60G70
Secondary: 62E20, 62G32

Rights: Copyright © 2014 Applied Probability Trust

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Vol.46 • No. 2 • June 2014
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