On generalized max-linear models and their statistical interpolation

2013/03/11 by Michael Falk, Falk, Michael, Martin R. Hofmann +3
Decision Sciences · Engineering · Physics and Astronomy · #60G70 #Control Systems and Identification #FOS: Mathematics #Model Reduction and Neural Networks #Probabilistic and Robust Engineering Design #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1303.2602

openalex publication_date 2013/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a way how to generate a max-stable process in C[0,1] from a max-stable random vector in \mathbb R^d by generalizing the max-linear model established by \citetwansto11. 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, reasonable prediction of max-stable processes in space becomes possible. A possible extension to arbitrary dimension is outlined.

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