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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
Random networks with heterogeneous reciprocity 具有异构互易的随机网络
3区 数学
Extremes Pub Date : 2023-09-25 DOI: 10.1007/s10687-023-00478-6
Tiandong Wang, Sidney Resnick
{"title":"Random networks with heterogeneous reciprocity","authors":"Tiandong Wang, Sidney Resnick","doi":"10.1007/s10687-023-00478-6","DOIUrl":"https://doi.org/10.1007/s10687-023-00478-6","url":null,"abstract":"","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135817312","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
Weighted weak convergence of the sequential tail empirical process for heteroscedastic time series with an application to extreme value index estimation 异方差时间序列序列尾经验过程的加权弱收敛性及其在极值指数估计中的应用
IF 1.3 3区 数学
Extremes Pub Date : 2023-08-24 DOI: 10.1007/s10687-023-00476-8
Tobias Jennessen, Axel Bücher
{"title":"Weighted weak convergence of the sequential tail empirical process for heteroscedastic time series with an application to extreme value index estimation","authors":"Tobias Jennessen, Axel Bücher","doi":"10.1007/s10687-023-00476-8","DOIUrl":"https://doi.org/10.1007/s10687-023-00476-8","url":null,"abstract":"","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"1 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43717133","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
Remembering Ross Leadbetter: some personal recollections 怀念罗斯·利德贝特：一些个人回忆
IF 1.3 3区 数学
Extremes Pub Date : 2023-04-10 DOI: 10.1007/s10687-023-00464-y
T. Hsing, H. Rootzén
{"title":"Remembering Ross Leadbetter: some personal recollections","authors":"T. Hsing, H. Rootzén","doi":"10.1007/s10687-023-00464-y","DOIUrl":"https://doi.org/10.1007/s10687-023-00464-y","url":null,"abstract":"","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"26 1","pages":"399 - 412"},"PeriodicalIF":1.3,"publicationDate":"2023-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47386584","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
A weighted composite log-likelihood approach to parametric estimation of the extreme quantiles of a distribution 分布极值分位数参数估计的加权复合对数似然方法
IF 1.3 3区 数学
Extremes Pub Date : 2023-03-29 DOI: 10.1007/s10687-023-00466-w
M. Stein
{"title":"A weighted composite log-likelihood approach to parametric estimation of the extreme quantiles of a distribution","authors":"M. Stein","doi":"10.1007/s10687-023-00466-w","DOIUrl":"https://doi.org/10.1007/s10687-023-00466-w","url":null,"abstract":"","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"26 1","pages":"469 - 507"},"PeriodicalIF":1.3,"publicationDate":"2023-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45244869","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: 1
Editorial: EVA 2021 data challenge on spatiotemporal prediction of wildfire extremes in the USA 社论：EVA 2021美国野火极端时空预测数据挑战
IF 1.3 3区 数学
Extremes Pub Date : 2023-03-27 DOI: 10.1007/s10687-023-00465-x
T. Opitz
{"title":"Editorial: EVA 2021 data challenge on spatiotemporal prediction of wildfire extremes in the USA","authors":"T. Opitz","doi":"10.1007/s10687-023-00465-x","DOIUrl":"https://doi.org/10.1007/s10687-023-00465-x","url":null,"abstract":"","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"26 1","pages":"241 - 250"},"PeriodicalIF":1.3,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49573895","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: 1
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