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


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.


Download Citation

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.


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

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

Primary: 60G70
Secondary: 62E20 , 62G32

Keywords: Extreme value statistics , incremental representation , Max-stable process , mixed moving maxima , peaks-over-threshold

Rights: Copyright © 2014 Applied Probability Trust


This article is only available to subscribers.
It is not available for individual sale.

Vol.46 • No. 2 • June 2014
Back to Top