Event-controlled constructions of random fields of maxima with non-max-stable dependence

TL;DR

This paper extends event-controlled max-stable random field constructions to non-max-stable dependence structures, providing a numerical approach and a parameter estimation method using Kendall's tau for modeling complex spatial dependencies.

Contribution

It introduces a novel extension of event-controlled constructions to non-max-stable dependence structures and proposes a Kendall's tau-based parameter estimation method.

Findings

The variant with a stationary process has parameters determined by event magnitude.

The random function scaling is exponentially related to event magnitude.

A practical method for parameter estimation using Kendall's tau is proposed.

Abstract

Max-stable random fields can be constructed according to Schlather (2002) with a random function or a stationary process and a kind of random event magnitude. These are applied for the modelling of natural hazards. We simply extend these event-controlled constructions to random fields of maxima with non-max-stable dependence structure (copula). The theory for the variant with a stationary process is obvious; the parameter(s) of its correlation function is/are determined by the event magnitude. The introduced variant with random functions can only be researched numerically. The scaling of the random function is exponentially determined by the event magnitude. The location parameter of the Gumbel margins depends only on this exponential function in the researched examples; the scale parameter of the margins is normalized. In addition, we propose a method for the parameter estimation for such constructions by using Kendall's tau. The spatial dependence in relation to the block size is considered therein. Finally, we briefly discuss some issues like the sampling.