Spatial dependence and space–time trend in extreme events

Einmahl, J. H. J., Ferreira, A., de Haan, L., Neves, C. ORCID: https://orcid.org/0000-0003-1201-5720 and Zhou, C. (2022) Spatial dependence and space–time trend in extreme events. Annals of Statistics, 50 (1). pp. 30-52. ISSN 2168-8966 doi: 10.1214/21-AOS2067

Abstract/Summary

The statistical theory of extremes is extended to independent multivariate observations that are non-stationary both over time and across space. The non-stationarity over time and space is controlled via the scedasis (tail scale) in the marginal distributions. Spatial dependence stems from multivariate extreme value theory. We establish asymptotic theory for both the weighted sequential tail empirical process and the weighted tail quantile process based on all observations, taken over time and space. The results yield two statistical tests for homoscedasticity in the tail, one in space and one in time. Further, we show that the common extreme value index can be estimated via a pseudo-maximum likelihood procedure based on pooling all (non-stationary and dependent) observations. Our leading example and application is rainfall in Northern Germany.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/104770
Identification Number/DOI	10.1214/21-AOS2067
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Institute of Mathematical Statistics
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