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Testing for changes in the tail behavior of Brown–Resnick Pareto processes

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  • Robert, Christian Y.

Abstract

We consider the class of r-Pareto processes defined on [0,1] whose max-stable counterparts are Brown–Resnick processes. The aim of this paper is to propose a test whether the extreme value index function of a r-Pareto process of this class remains constant over [0,1]. We assume that we observe several independent r-Pareto processes over equispaced grids of [0,1] but with possibly heterogeneous grid resolutions. We build a test based on the normalized approximate total variations of the paths of these processes. We provide its properties under infill asymptotics and assess its finite sample performance through simulation experiments. We discuss how to proceed for random processes that belong to the domain of attraction of Brown–Resnick r-Pareto processes and illustrate the approach with an application to wind speed data from Germany.

Suggested Citation

  • Robert, Christian Y., 2022. "Testing for changes in the tail behavior of Brown–Resnick Pareto processes," Stochastic Processes and their Applications, Elsevier, vol. 144(C), pages 312-368.
    • Handle: RePEc:eee:spapps:v:144:y:2022:i:c:p:312-368
    DOI: 10.1016/j.spa.2021.11.009
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    References listed on IDEAS

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    1. R de Fondeville & A C Davison, 2018. "High-dimensional peaks-over-threshold inference," Biometrika, Biometrika Trust, vol. 105(3), pages 575-592.
    2. John H. J. Einmahl & Anna Kiriliouk & Andrea Krajina & Johan Segers, 2016. "An M-estimator of spatial tail dependence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 275-298, January.
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