September 2015 On generalized max-linear models and their statistical interpolation
Michael Falk, Martin Hofmann, Maximilian Zott
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J. Appl. Probab. 52(3): 736-751 (September 2015). DOI: 10.1239/jap/1445543843


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.


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Michael Falk. Martin Hofmann. Maximilian Zott. "On generalized max-linear models and their statistical interpolation." J. Appl. Probab. 52 (3) 736 - 751, September 2015.


Published: September 2015
First available in Project Euclid: 22 October 2015

zbMATH: 1336.60101
MathSciNet: MR3414988
Digital Object Identifier: 10.1239/jap/1445543843

Primary: 60G70

Keywords: D-norm , generalized Pareto process , max-linear model , Max-stable process , Multivariate extreme value distribution , Multivariate generalized Pareto distribution , prediction of generalized Pareto process , prediction of max-stable process

Rights: Copyright © 2015 Applied Probability Trust


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Vol.52 • No. 3 • September 2015
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