Journal of Applied Probability

On generalized max-linear models and their statistical interpolation

Michael Falk, Martin Hofmann, and Maximilian Zott

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Abstract

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.

Article information

Source
J. Appl. Probab., Volume 52, Number 3 (2015), 736-751.

Dates
First available in Project Euclid: 22 October 2015

Permanent link to this document
https://projecteuclid.org/euclid.jap/1445543843

Digital Object Identifier
doi:10.1239/jap/1445543843

Mathematical Reviews number (MathSciNet)
MR3414988

Zentralblatt MATH identifier
1336.60101

Subjects
Primary: 60G70: Extreme value theory; extremal processes

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

Citation

Falk, Michael; Hofmann, Martin; Zott, Maximilian. On generalized max-linear models and their statistical interpolation. J. Appl. Probab. 52 (2015), no. 3, 736--751. doi:10.1239/jap/1445543843. https://projecteuclid.org/euclid.jap/1445543843


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