论文标题
阈值分析的功能峰值
Functional Peaks-over-threshold Analysis
论文作者
论文摘要
使用广义帕累托分布的峰值阈值分析广泛应用于单变量随机变量的尾巴建模，但是当使用单变量结果研究复杂的极端事件时，可能会丢失很多信息。在本文中，我们将阈值分析扩展到功能数据的极端。使用功能性$ r $定义的阈值超出阈值是由广义$ r $ - pareto流程建模的，这是对广义帕累托分布的功能概括，涵盖了尾巴概率衰减的三个经典制度，这是$ r $ $ r $ - exceceedeccepercepercepercepercepercepecceence copecceceedcess的唯一可能的连续限制。我们提供有关广义$ r $ pareto流程的施工规则，仿真算法和推理程序，讨论模型验证，并使用新的方法来研究极端的欧洲风暴和大量的空间降雨。
Peaks-over-threshold analysis using the generalized Pareto distribution is widely applied in modelling tails of univariate random variables, but much information may be lost when complex extreme events are studied using univariate results. In this paper, we extend peaks-over-threshold analysis to extremes of functional data. Threshold exceedances defined using a functional $r$ are modelled by the generalized $r$-Pareto process, a functional generalization of the generalized Pareto distribution that covers the three classical regimes for the decay of tail probabilities, and that is the only possible continuous limit for $r$-exceedances of a properly rescaled process. We give construction rules, simulation algorithms and inference procedures for generalized $r$-Pareto processes, discuss model validation, and use the new methodology to study extreme European windstorms and heavy spatial rainfall.
