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Modelling the distribution of the cluster maxima of exceedances of subasymptotic thresholds

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  • Emma F. Eastoe
  • Jonathan A. Tawn

Abstract

A standard approach to model the extreme values of a stationary process is the peaks over threshold method, which consists of imposing a high threshold, identifying clusters of exceedances of this threshold and fitting the maximum value from each cluster using the generalized Pareto distribution. This approach is strongly justified by underlying asymptotic theory. We propose an alternative model for the distribution of the cluster maxima that accounts for the subasymptotic theory of extremes of a stationary process. This new distribution is a product of two terms, one for the marginal distribution of exceedances and the other for the dependence structure of the exceedance values within a cluster. We illustrate the improvement in fit, measured by the root mean square error of the estimated quantiles, offered by the new distribution over the peaks over thresholds analysis using simulated and hydrological data, and we suggest a diagnostic tool to help identify when the proposed model is likely to lead to an improved fit. Copyright 2012, Oxford University Press.

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  • Emma F. Eastoe & Jonathan A. Tawn, 2012. "Modelling the distribution of the cluster maxima of exceedances of subasymptotic thresholds," Biometrika, Biometrika Trust, vol. 99(1), pages 43-55.
    • Handle: RePEc:oup:biomet:v:99:y:2012:i:1:p:43-55
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    File URL: http://hdl.handle.net/10.1093/biomet/asr078
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    Cited by:

    1. 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.
    2. Chiapino, Mael & Sabourin, Anne & Segers, Johan, 2018. "Identifying groups of variables with the potential of being large simultaneously," LIDAM Discussion Papers ISBA 2018006, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Xiaoting Li & Christian Genest & Jonathan Jalbert, 2021. "A self‐exciting marked point process model for drought analysis," Environmetrics, John Wiley & Sons, Ltd., vol. 32(8), December.
    4. Hugo C. Winter & Jonathan A. Tawn, 2016. "Modelling heatwaves in central France: a case-study in extremal dependence," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(3), pages 345-365, April.
    5. Gloria Buriticá & Philippe Naveau, 2023. "Stable sums to infer high return levels of multivariate rainfall time series," Environmetrics, John Wiley & Sons, Ltd., vol. 34(4), June.
    6. Keef, Caroline & Papastathopoulos, Ioannis & Tawn, Jonathan A., 2013. "Estimation of the conditional distribution of a multivariate variable given that one of its components is large: Additional constraints for the Heffernan and Tawn model," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 396-404.
    7. Richards, Jordan & Tawn, Jonathan A., 2022. "On the tail behaviour of aggregated random variables," Journal of Multivariate Analysis, Elsevier, vol. 192(C).

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