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Dependence modelling for spatial extremes

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  • Jennifer L. Wadsworth
  • Jonathan A. Tawn

Abstract

Current dependence models for spatial extremes are based upon max-stable processes. Within this class, there are few inferentially viable models available, and we propose one further model. More problematic are the restrictive assumptions that must be made when using max-stable processes to model dependence for spatial extremes: it must be assumed that the dependence structure of the observed extremes is compatible with a limiting model that holds for all events more extreme than those that have already occurred. This problem has long been acknowledged in the context of finite-dimensional multivariate extremes, in particular when data display dependence at observable levels, but are independent in the limit. We propose a flexible class of models that is suitable for such data in a spatial context. In addition, we consider the situation where the extremal dependence structure may vary with distance. We apply our models to spatially referenced significant wave height data from the North Sea, finding evidence that their extremal structure is not compatible with a limiting dependence model. Copyright 2012, Oxford University Press.

Suggested Citation

  • Jennifer L. Wadsworth & Jonathan A. Tawn, 2012. "Dependence modelling for spatial extremes," Biometrika, Biometrika Trust, vol. 99(2), pages 253-272.
    • Handle: RePEc:oup:biomet:v:99:y:2012:i:2:p:253-272
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    File URL: http://hdl.handle.net/10.1093/biomet/asr080
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    Cited by:

    1. Marta Ferreira & Helena Ferreira, 2017. "Analyzing the Gaver—Lewis Pareto Process under an Extremal Perspective," Risks, MDPI, vol. 5(3), pages 1-12, June.
    2. Curtis B. Storlie & Brian J. Reich & William N. Rust & Lawrence O. Ticknor & Amanda M. Bonnie & Andrew J. Montoya & Sarah E. Michalak, 2017. "Spatiotemporal Modeling of Node Temperatures in Supercomputers," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 92-108, January.
    3. Papastathopoulos, Ioannis & Tawn, Jonathan A., 2016. "Conditioned limit laws for inverted max-stable processes," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 214-228.
    4. R. Shooter & E. Ross & A. Ribal & I. R. Young & P. Jonathan, 2021. "Spatial dependence of extreme seas in the North East Atlantic from satellite altimeter measurements," Environmetrics, John Wiley & Sons, Ltd., vol. 32(4), June.
    5. Moreno Bevilacqua & Christian Caamaño‐Carrillo & Carlo Gaetan, 2020. "On modeling positive continuous data with spatiotemporal dependence," Environmetrics, John Wiley & Sons, Ltd., vol. 31(7), November.
    6. Robert, Christian Y., 2013. "Some new classes of stationary max-stable random fields," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1496-1503.
    7. Ferreira, Helena & Ferreira, Marta, 2018. "Multidimensional extremal dependence coefficients," Statistics & Probability Letters, Elsevier, vol. 133(C), pages 1-8.
    8. Manaf Ahmed & Véronique Maume‐Deschamps & Pierre Ribereau, 2022. "Recognizing a spatial extreme dependence structure: A deep learning approach," Environmetrics, John Wiley & Sons, Ltd., vol. 33(4), June.
    9. Lee Fawcett & David Walshaw, 2014. "Estimating the probability of simultaneous rainfall extremes within a region: a spatial approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(5), pages 959-976, May.
    10. Samuel A. Morris & Brian J. Reich & Emeric Thibaud & Daniel Cooley, 2017. "A space-time skew-t model for threshold exceedances," Biometrics, The International Biometric Society, vol. 73(3), pages 749-758, September.
    11. Raphaël Huser & Marc G. Genton, 2016. "Non-Stationary Dependence Structures for Spatial Extremes," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(3), pages 470-491, September.
    12. Martins, Ana Paula & Ferreira, Helena & Ferreira, Marta, 2022. "A new random field on lattices," Statistics & Probability Letters, Elsevier, vol. 186(C).
    13. A. Abu-Awwad & V. Maume-Deschamps & P. Ribereau, 2021. "Semiparametric estimation for space-time max-stable processes: an F-madogram-based approach," Statistical Inference for Stochastic Processes, Springer, vol. 24(2), pages 241-276, July.
    14. Padoan, Simone A., 2013. "Extreme dependence models based on event magnitude," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 1-19.
    15. Richards, Jordan & Tawn, Jonathan A., 2022. "On the tail behaviour of aggregated random variables," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    16. Kereszturi, Mónika & Tawn, Jonathan, 2017. "Properties of extremal dependence models built on bivariate max-linearity," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 52-71.
    17. Jordan Richards & Jennifer L. Wadsworth, 2021. "Spatial deformation for nonstationary extremal dependence," Environmetrics, John Wiley & Sons, Ltd., vol. 32(5), August.
    18. A. Abu-Awwad & V. Maume-Deschamps & P. Ribereau, 2020. "Fitting spatial max-mixture processes with unknown extremal dependence class: an exploratory analysis tool," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 479-522, June.
    19. Ji-Eun Choi & Dong Wan Shin, 2022. "Quantile correlation coefficient: a new tail dependence measure," Statistical Papers, Springer, vol. 63(4), pages 1075-1104, August.

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