On the spatial extent of extreme threshold exceedances
- Others:
- Université de Lausanne = University of Lausanne (UNIL)
- Laboratoire Jean Alexandre Dieudonné (LJAD) ; Université Nice Sophia Antipolis (1965 - 2019) (UNS)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UniCA)
- Biostatistique et Processus Spatiaux (BioSP) ; Institut National de Recherche pour l'Agriculture, l'Alimentation et l'Environnement (INRAE)
- ANR-19-P3IA-0002,3IA@cote d'azur,3IA Côte d'Azur(2019)
- ANR-22-EXIR-0008,Plateformes,Plateformes numériques - Une architecture distribuée de données et de services concourrant à la mise en œuvre de scénarios de risques(2022)
Description
We introduce the extremal range, a local statistic for studying the spatial extent of extreme events in random fields on $\mathbb{R}^d$. Conditioned on exceedance of a high threshold at a location s, the extremal range at $s$ is the random variable defined as the smallest distance from $s\in\mathbb{R}^d$ to a location where there is a nonexceedance. We leverage tools from excursion-set theory, such as Lipschitz-Killing curvatures, to express distributional properties of the extremal range, including asymptotics for small distances and high thresholds. The extremal range captures the rate at which the spatial extent of conditional extreme events scales for increasingly high thresholds, and we relate its distributional properties with the well-known bivariate tail dependence coefficient and the extremal index of time series in Extreme-Value Theory. We calculate theoretical extremal-range properties for commonly used models, such as Gaussian or regularly varying random fields. Numerical studies illustrate that, when the extremal range is estimated from discretized excursion sets observed on compact observation windows, the distribution of the resulting estimators appropriately reproduces the theoretically derived links with the Lipschitz-Killing curvature densities.
Abstract
International audience
Additional details
- URL
- https://hal.science/hal-04735500
- URN
- urn:oai:HAL:hal-04735500v1
- Origin repository
- UNICA