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Spatial extremes and stochastic geometry for Gaussian-based peaks-over-threshold processes 基于高斯的峰过阈值过程的空间极值和随机几何
IF 1.3 3区 数学
Extremes Pub Date : 2024-05-01 DOI: 10.1007/s10687-024-00487-z
Elena Di Bernardino, Anne Estrade, Thomas Opitz
{"title":"Spatial extremes and stochastic geometry for Gaussian-based peaks-over-threshold processes","authors":"Elena Di Bernardino, Anne Estrade, Thomas Opitz","doi":"10.1007/s10687-024-00487-z","DOIUrl":"https://doi.org/10.1007/s10687-024-00487-z","url":null,"abstract":"<p>Geometric properties of exceedance regions above a given quantile level provide meaningful theoretical and statistical characterizations for stochastic processes defined on Euclidean domains. Many theoretical results have been obtained for excursions of Gaussian processes and include expected values of the so-called Lipschitz–Killing curvatures (LKCs), such as the area, perimeter and Euler characteristic in two-dimensional Euclidean space. In this paper, we derive novel results for the expected LKCs of excursion sets of more general processes whose construction is based on location or scale mixtures of a Gaussian process, which means that the mean or the standard deviation, respectively, of a stationary Gaussian process is a random variable. We first present exact formulas for peaks-over-threshold-stable limit processes (so-called Pareto processes) arising from the use of Gaussian or log-Gaussian spectral functions in the spectral construction of max-stable processes. These peaks-over-threshold limits are known to arise for Gaussian location or scale mixtures if the mixing distributions satisfies certain regular-variation properties. As a second important result, we show that expected LKCs of excursion sets of such general mixture processes converge to the corresponding expressions of their Pareto process limits. We further provide exact subasymptotic formulas of expected LKCs for various specific choices of the distribution of the mixing variable. Finally, we discuss consistent empirical estimation of LKCs of exceedance regions and implement numerical experiments to illustrate the rate of convergence towards asymptotic expressions. An application to daily temperature data simulated by climate models for the period 1951–2005 over a regular pixel grid covering continental France showcases the practical utility of the new results.</p>","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"101 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140833322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stochastic ordering in multivariate extremes 多元极值中的随机排序
IF 1.3 3区 数学
Extremes Pub Date : 2024-05-01 DOI: 10.1007/s10687-024-00486-0
Michela Corradini, Kirstin Strokorb
{"title":"Stochastic ordering in multivariate extremes","authors":"Michela Corradini, Kirstin Strokorb","doi":"10.1007/s10687-024-00486-0","DOIUrl":"https://doi.org/10.1007/s10687-024-00486-0","url":null,"abstract":"<p>The article considers the multivariate stochastic orders of upper orthants, lower orthants and positive quadrant dependence (PQD) among simple max-stable distributions and their exponent measures. It is shown for each order that it holds for the max-stable distribution if and only if it holds for the corresponding exponent measure. The finding is non-trivial for upper orthants (and hence PQD order). From dimension <span>(dge 3)</span> these three orders are not equivalent and a variety of phenomena can occur. However, every simple max-stable distribution PQD-dominates the corresponding independent model and is PQD-dominated by the fully dependent model. Among parametric models the asymmetric Dirichlet family and the Hüsler-Reiß family turn out to be PQD-ordered according to the natural order within their parameter spaces. For the Hüsler-Reiß family this holds true even for the supermodular order.</p>","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"41 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140842299","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generalized pareto regression trees for extreme event analysis 用于极端事件分析的广义帕累托回归树
IF 1.3 3区 数学
Extremes Pub Date : 2024-03-23 DOI: 10.1007/s10687-024-00485-1
Sébastien Farkas, Antoine Heranval, Olivier Lopez, Maud Thomas
{"title":"Generalized pareto regression trees for extreme event analysis","authors":"Sébastien Farkas, Antoine Heranval, Olivier Lopez, Maud Thomas","doi":"10.1007/s10687-024-00485-1","DOIUrl":"https://doi.org/10.1007/s10687-024-00485-1","url":null,"abstract":"<p>This paper derives finite sample results to assess the consistency of Generalized Pareto regression trees introduced by Farkas et al. (Insur. Math. Econ. 98:92–105, 2021) as tools to perform extreme value regression for heavy-tailed distributions. This procedure allows the constitution of classes of observations with similar tail behaviors depending on the value of the covariates, based on a recursive partition of the sample and simple model selection rules. The results we provide are obtained from concentration inequalities, and are valid for a finite sample size. A misspecification bias that arises from the use of a “Peaks over Threshold” approach is also taken into account. Moreover, the derived properties legitimate the pruning strategies, that is the model selection rules, used to select a proper tree that achieves a compromise between simplicity and goodness-of-fit. The methodology is illustrated through a simulation study, and a real data application in insurance for natural disasters.</p>","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"16 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140197074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On approximating dependence function and its derivatives 关于近似依存函数及其导数
IF 1.3 3区 数学
Extremes Pub Date : 2024-03-15 DOI: 10.1007/s10687-024-00484-2
Nader Tajvidi
{"title":"On approximating dependence function and its derivatives","authors":"Nader Tajvidi","doi":"10.1007/s10687-024-00484-2","DOIUrl":"https://doi.org/10.1007/s10687-024-00484-2","url":null,"abstract":"<p>Bivariate extreme value distributions can be used to model dependence of observations from random variables in extreme levels. There is no finite dimensional parametric family for these distributions, but they can be characterized by a certain one-dimensional function which is known as Pickands dependence function. In many applications the general approach is to estimate the dependence function with a non-parametric method and then conduct further analysis based on the estimate. Although this approach is flexible in the sense that it does not impose any special structure on the dependence function, its main drawback is that the estimate is not available in a closed form. This paper provides some theoretical results which can be used to find a closed form approximation for an exact or an estimate of a twice differentiable dependence function and its derivatives. We demonstrate the methodology by calculating approximations for symmetric and asymmetric logistic dependence functions and their second derivatives. We show that the theory can be even applied to approximating a non-parametric estimate of dependence function using a convex optimization algorithm. Other discussed applications include a procedure for testing whether an estimate of dependence function can be assumed to be symmetric and estimation of the concordance measures of a bivariate extreme value distribution. Finally, an Australian annual maximum temperature dataset is used to illustrate how the theory can be used to build semi-infinite and compact predictions regions.</p>","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"148 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154269","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Extremes for stationary regularly varying random fields over arbitrary index sets 任意索引集上静止规则变化随机场的极值
IF 1.3 3区 数学
Extremes Pub Date : 2024-01-25 DOI: 10.1007/s10687-023-00481-x
Riccardo Passeggeri, Olivier Wintenberger
{"title":"Extremes for stationary regularly varying random fields over arbitrary index sets","authors":"Riccardo Passeggeri, Olivier Wintenberger","doi":"10.1007/s10687-023-00481-x","DOIUrl":"https://doi.org/10.1007/s10687-023-00481-x","url":null,"abstract":"<p>We consider the clustering of extremes for stationary regularly varying random fields over arbitrary growing index sets. We study sufficient assumptions on the index set such that the limit of the point processes of the exceedances above a high threshold exists. Under the so-called anti-clustering condition, the extremal dependence is only local. Thus the index set can have a general form compared to previous literature (Basrak and Planinić in Bernoulli 27(2):1371–1408, 2021; Stehr and Rønn-Nielsen in Extremes 24(4):753–795, 2021). However, we cannot describe the clustering of extreme values in terms of the usual spectral tail measure (Wu and Samorodnitsky in Stochastic Process Appl 130(7):4470–4492, 2020) except for hyperrectangles or index sets in the lattice case. Using the recent extension of the spectral measure for star-shaped equipped space (Segers et al. in Extremes 20:539–566, 2017), the <span>(Upsilon)</span>-spectral tail measure provides a natural extension that describes the clustering effect in full generality.</p>","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"9 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139552332","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Extremes of locally-homogenous vector-valued Gaussian processes 局部同质矢量值高斯过程的极值
IF 1.3 3区 数学
Extremes Pub Date : 2024-01-08 DOI: 10.1007/s10687-023-00483-9
Pavel Ievlev
{"title":"Extremes of locally-homogenous vector-valued Gaussian processes","authors":"Pavel Ievlev","doi":"10.1007/s10687-023-00483-9","DOIUrl":"https://doi.org/10.1007/s10687-023-00483-9","url":null,"abstract":"<p>In this paper, we study the asymptotical behaviour of high exceedence probabilities for centered continuous <span>(mathbb {R}^n)</span>-valued Gaussian random field <span>(varvec{X})</span> with covariance matrix satisfying <span>(Sigma - R ( t + s, t ) sim sum _{l = 1}^n B_l ( t ) , | s_l |^{alpha _l})</span> as <span>(s downarrow 0)</span>. Such processes occur naturally as time transformations of homogenous random fields, and we present two asymptotic results of this nature as applications of our findings. The technical novelty of our proof consists in showing that the Slepian-Gordon inequality technique, essential in the univariate case, can also be successfully applied in the multivariate setup. This is noteworthy because this technique was previously believed to be inaccessible in this particular context.</p>","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"80 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139396792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Point process convergence for symmetric functions of high-dimensional random vectors 高维随机向量对称函数的点过程收敛性
IF 1.3 3区 数学
Extremes Pub Date : 2023-12-20 DOI: 10.1007/s10687-023-00482-w
Johannes Heiny, Carolin Kleemann
{"title":"Point process convergence for symmetric functions of high-dimensional random vectors","authors":"Johannes Heiny, Carolin Kleemann","doi":"10.1007/s10687-023-00482-w","DOIUrl":"https://doi.org/10.1007/s10687-023-00482-w","url":null,"abstract":"<p>The convergence of a sequence of point processes with dependent points, defined by a symmetric function of iid high-dimensional random vectors, to a Poisson random measure is proved. This also implies the convergence of the joint distribution of a fixed number of upper order statistics. As applications of the result a generalization of maximum convergence to point process convergence is given for simple linear rank statistics, rank-type U-statistics and the entries of sample covariance matrices.</p>","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"32 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138825376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Regional pooling in extreme event attribution studies: an approach based on multiple statistical testing 极端事件归因研究中的区域集合：基于多重统计检验的方法
IF 1.3 3区 数学
Extremes Pub Date : 2023-12-16 DOI: 10.1007/s10687-023-00480-y
Leandra Zanger, Axel Bücher, Frank Kreienkamp, Philip Lorenz, Jordis S. Tradowsky
{"title":"Regional pooling in extreme event attribution studies: an approach based on multiple statistical testing","authors":"Leandra Zanger, Axel Bücher, Frank Kreienkamp, Philip Lorenz, Jordis S. Tradowsky","doi":"10.1007/s10687-023-00480-y","DOIUrl":"https://doi.org/10.1007/s10687-023-00480-y","url":null,"abstract":"<p>Statistical methods are proposed to select homogeneous regions when analyzing spatial block maxima data, such as in extreme event attribution studies. Here, homogeneitity refers to the fact that marginal model parameters are the same at different locations from the region. The methods are based on classical hypothesis testing using Wald-type test statistics, with critical values obtained from suitable parametric bootstrap procedures and corrected for multiplicity. A large-scale Monte Carlo simulation study finds that the methods are able to accurately identify homogeneous locations, and that pooling the selected locations improves the accuracy of subsequent statistical analyses. The approach is illustrated with a case study on precipitation extremes in Western Europe. The methods are implemented in an R package that allows for easy application in future extreme event attribution studies.</p>","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"71 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138684102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Tail adversarial stability for regularly varying linear processes and their extensions 规则变化线性过程的尾部对抗稳定性及其扩展
IF 1.3 3区 数学
Extremes Pub Date : 2023-12-13 DOI: 10.1007/s10687-023-00477-7
Shuyang Bai, Ting Zhang
{"title":"Tail adversarial stability for regularly varying linear processes and their extensions","authors":"Shuyang Bai, Ting Zhang","doi":"10.1007/s10687-023-00477-7","DOIUrl":"https://doi.org/10.1007/s10687-023-00477-7","url":null,"abstract":"<p>The notion of tail adversarial stability has been proven useful in obtaining limit theorems for tail dependent time series. Its implication and advantage over the classical strong mixing framework has been examined for max-linear processes, but not yet studied for additive linear processes. In this article, we fill this gap by verifying the tail adversarial stability condition for regularly varying additive linear processes. We in addition consider extensions of the result to a stochastic volatility generalization and to a max-linear counterpart. We also address the invariance of tail adversarial stability under monotone transforms. Some implications for limit theorems in statistical context are also discussed.</p>","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"86 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138631470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Causality in extremes of time series 极端时间序列的因果关系
3区 数学
Extremes Pub Date : 2023-10-31 DOI: 10.1007/s10687-023-00479-5
Juraj Bodik, Milan Paluš, Zbyněk Pawlas
{"title":"Causality in extremes of time series","authors":"Juraj Bodik, Milan Paluš, Zbyněk Pawlas","doi":"10.1007/s10687-023-00479-5","DOIUrl":"https://doi.org/10.1007/s10687-023-00479-5","url":null,"abstract":"Abstract Consider two stationary time series with heavy-tailed marginal distributions. We aim to detect whether they have a causal relation, that is, if a change in one causes a change in the other. Usual methods for causal discovery are not well suited if the causal mechanisms only appear during extreme events. We propose a framework to detect a causal structure from the extremes of time series, providing a new tool to extract causal information from extreme events. We introduce the causal tail coefficient for time series, which can identify asymmetrical causal relations between extreme events under certain assumptions. This method can handle nonlinear relations and latent variables. Moreover, we mention how our method can help estimate a typical time difference between extreme events. Our methodology is especially well suited for large sample sizes, and we show the performance on the simulations. Finally, we apply our method to real-world space-weather and hydro-meteorological datasets.","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"2008 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135813783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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