Simpson, Emma S;
Tawn, Jonathan A;
(2024)
Inference for new environmental contours using extreme value analysis.
Journal of Agricultural, Biological, and Environmental Statistics
10.1007/s13253-024-00612-2.
(In press).
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Abstract
Environmental contours are often used in engineering applications to describe risky combinations of variables according to some definition of an exceedance probability. These contours can be used to both understand multivariate extreme events in environmental processes and mitigate against their effects, e.g., in the design of structures. Such ideas are also useful in other disciplines, with the types of extreme events of interest depending on the context. Despite clear connections with extreme value modelling, much of this methodology has so far not been exploited in the estimation of environmental contours; in this work, we provide a way to unify these areas. We focus on the bivariate case, introducing two new definitions of environmental contours. We develop techniques for their inference which exploit a nonstandard radial and angular decomposition of the variables, building on previous work for estimating limit sets. Specifically, we model the upper tails of the radial distribution using a generalised Pareto distribution, with adaptable smoothing of the parameters of this distribution. Our methods work equally well for asymptotically independent and asymptotically dependent variables, so do not require us to distinguish between different joint tail forms. Simulations demonstrate reasonable success of the estimation procedure, and we apply our approach to an air pollution data set, which is of interest in the context of environmental impacts on health.
| Type: | Article |
|---|---|
| Title: | Inference for new environmental contours using extreme value analysis |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s13253-024-00612-2 |
| Publisher version: | https://doi.org/10.1007/s13253-024-00612-2 |
| Language: | English |
| Additional information: | This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| Keywords: | Bivariate extremes; Environmental contours; Generalised additive model; Generalised Pareto distribution; Structure function |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10186227 |
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