Clustering of extreme values: estimation and application

IF 1.4 4区 数学 Q2 STATISTICS & PROBABILITY Asta-Advances in Statistical Analysis Pub Date : 2023-03-31 DOI:10.1007/s10182-023-00474-y
Marta Ferreira
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Abstract

The extreme value theory (EVT) encompasses a set of methods that allow inferring about the risk inherent to various phenomena in the scope of economic, financial, actuarial, environmental, hydrological, climatic sciences, as well as various areas of engineering. In many situations the clustering effect of high values may have an impact on the risk of occurrence of extreme phenomena. For example, extreme temperatures that last over time and result in drought situations, the permanence of intense rains leading to floods, stock markets in successive falls and consequent catastrophic losses. The extremal index is a measure of EVT associated with the degree of clustering of extreme values. In many situations, and under certain conditions, it corresponds to the arithmetic inverse of the average size of high-value clusters. The estimation of the extremal index generally entails two sources of uncertainty: the level at which high observations are considered and the identification of clusters. There are several contributions in the literature on the estimation of the extremal index, including methodologies to overcome the aforementioned sources of uncertainty. In this work we will revisit several existing estimators, apply automatic choice methods, both for the threshold and for the clustering parameter, and compare the performance of the methods. We will end with an application to meteorological data.

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极值聚类:估计和应用。
极值理论(EVT)包括一套方法,可以推断经济、金融、精算、环境、水文、气候科学以及各种工程领域中各种现象所固有的风险。在许多情况下,高值的聚集效应可能会对极端现象发生的风险产生影响。例如,持续一段时间并导致干旱的极端温度,导致洪水的持续暴雨,股市连续下跌,以及随之而来的灾难性损失。极值指数是与极值的聚类程度相关联的EVT的度量。在许多情况下,在某些条件下,它对应于高值集群平均大小的算术逆。极值指数的估计通常包含两个不确定性来源:考虑高观测值的水平和聚类的识别。文献中有一些关于极值指数估计的贡献,包括克服上述不确定性来源的方法。在这项工作中,我们将重新审视几种现有的估计量,应用阈值和聚类参数的自动选择方法,并比较这些方法的性能。最后我们将介绍气象数据的应用。
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来源期刊
Asta-Advances in Statistical Analysis
Asta-Advances in Statistical Analysis 数学-统计学与概率论
CiteScore
2.20
自引率
14.30%
发文量
39
审稿时长
>12 weeks
期刊介绍: AStA - Advances in Statistical Analysis, a journal of the German Statistical Society, is published quarterly and presents original contributions on statistical methods and applications and review articles.
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