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On generalized max-linear models and their statistical interpolation

Part of: Stochastic processes

Published online by Cambridge University Press:  30 March 2016

Michael Falk ,
Martin Hofmann  and
Maximilian Zott
Michael Falk*
Affiliation:
University of Wurzburg
Martin Hofmann*
Affiliation:
University of Wurzburg
Maximilian Zott*
Affiliation:
University of Wurzburg
*
∗ Postal address: Institute of Mathematics, University of Wurzburg, Emil-Fischer-Str. 30, 97074 Würzburg, Germany.
∗ Postal address: Institute of Mathematics, University of Wurzburg, Emil-Fischer-Str. 30, 97074 Würzburg, Germany.
∗ Postal address: Institute of Mathematics, University of Wurzburg, Emil-Fischer-Str. 30, 97074 Würzburg, Germany.
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Abstract

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We propose a method to generate a max-stable process in C[0, 1] from a max-stable random vector in Rd by generalizing the max-linear model established by Wang and Stoev (2011). For this purpose, an interpolation technique that preserves max-stability is proposed. It turns out that if the random vector follows some finite-dimensional distribution of some initial max-stable process, the approximating processes converge uniformly to the original process and the pointwise mean-squared error can be represented in a closed form. The obtained results carry over to the case of generalized Pareto processes. The introduced method enables the reconstruction of the initial process only from a finite set of observation points and, thus, a reasonable prediction of max-stable processes in space becomes possible. A possible extension to arbitrary dimensions is outlined.

Keywords

Multivariate extreme value distributionmultivariate generalized Pareto distributionmax-stable processgeneralized Pareto processD-normmax-linear modelprediction of max-stable processprediction of generalized Pareto process

MSC classification

Primary: 60G70: Extreme value theory; extremal processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 52 , Issue 3 , September 2015 , pp. 736 - 751
Copyright
Copyright © 2015 by the Applied Probability Trust 

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