IF 1.3 3区数学

Extremes Pub Date : 2024-09-11 DOI: 10.1007/s10687-024-00497-x

Seungwoo Kang, Kyusoon Kim, Youngwook Kwon, Seeun Park, Seoncheol Park, Ha-Young Shin, Joonpyo Kim, Hee-Seok Oh

{"title":"Semiparametric approaches for the inference of univariate and multivariate extremes","authors":"Seungwoo Kang, Kyusoon Kim, Youngwook Kwon, Seeun Park, Seoncheol Park, Ha-Young Shin, Joonpyo Kim, Hee-Seok Oh","doi":"10.1007/s10687-024-00497-x","DOIUrl":"https://doi.org/10.1007/s10687-024-00497-x","url":null,"abstract":"In this paper, we present several semiparametric approaches for the inference of univariate and multivariate extremes to resolve the tasks from the EVA (2023) Conference Data Challenge. We implement generalized additive models to capture the flexible relationship for point and interval estimations of the conditional quantiles. We also adopt (L^{p})-quantile to estimate the marginal quantiles of extreme levels. To predict probabilities of multivariate extreme events, we implement conditional methods by Heffernan and Tawn (Royal J. Stat. Soc.: Ser. B (Statistical Methodology) 66(3), 497–546, 2004) and Keef et al. (J. Multivar. Anal. 115, 396–404, 2013). We further validate predicted models, evaluating their performance scores constructed based on the notion of an equally extreme level of quantiles and cross-validation to select the best estimates to achieve high accuracy. When estimating the excess probability of 50-dimensional data, we cluster variables with high correlation after simple data exploration and combine the results obtained from each cluster. Finally, we also provide post-mortem analysis based on the ground truth.","PeriodicalId":49274,"journal":{"name":"Extremes","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142182388","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

Modern extreme value statistics for Utopian extremes. EVA (2023) Conference Data Challenge: Team Yalla 乌托邦极值的现代极值统计。EVA (2023) 会议数据挑战赛：雅拉团队

IF 1.3 3区数学

Extremes Pub Date : 2024-09-07 DOI: 10.1007/s10687-024-00496-y

Jordan Richards, Noura Alotaibi, Daniela Cisneros, Yan Gong, Matheus B. Guerrero, Paolo Victor Redondo, Xuanjie Shao

{"title":"Modern extreme value statistics for Utopian extremes. EVA (2023) Conference Data Challenge: Team Yalla","authors":"Jordan Richards, Noura Alotaibi, Daniela Cisneros, Yan Gong, Matheus B. Guerrero, Paolo Victor Redondo, Xuanjie Shao","doi":"10.1007/s10687-024-00496-y","DOIUrl":"https://doi.org/10.1007/s10687-024-00496-y","url":null,"abstract":"Capturing the extremal behaviour of data often requires bespoke marginal and dependence models which are grounded in rigorous asymptotic theory, and hence provide reliable extrapolation into the upper tails of the data-generating distribution. We present a modern toolbox of four methodological frameworks, motivated by classical extreme value theory, that can be used to accurately estimate extreme exceedance probabilities or the corresponding level in either a univariate or multivariate setting. Our frameworks were used to facilitate the winning contribution of Team Yalla to the EVA (2023) Conference Data Challenge, which was organised for the 13(^text {th}) International Conference on Extreme Value Analysis. This competition comprised seven teams competing across four separate sub-challenges, with each requiring the modelling of data simulated from known, yet highly complex, statistical distributions, and extrapolation far beyond the range of the available samples in order to predict probabilities of extreme events. Data were constructed to be representative of real environmental data, sampled from the fantasy country of “Utopia”.","PeriodicalId":49274,"journal":{"name":"Extremes","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142182389","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 utopic adventure in the modelling of conditional univariate and multivariate extremes 条件单变量和多变量极值建模中的乌托邦式探险

IF 1.3 3区数学

Extremes Pub Date : 2024-09-04 DOI: 10.1007/s10687-024-00493-1

Léo R. Belzile, Arnab Hazra, Rishikesh Yadav

引用次数: 0

Cross-validation on extreme regions 极端区域交叉验证

IF 1.3 3区数学

Extremes Pub Date : 2024-09-03 DOI: 10.1007/s10687-024-00495-z

Anass Aghbalou, Patrice Bertail, François Portier, Anne Sabourin

{"title":"Cross-validation on extreme regions","authors":"Anass Aghbalou, Patrice Bertail, François Portier, Anne Sabourin","doi":"10.1007/s10687-024-00495-z","DOIUrl":"https://doi.org/10.1007/s10687-024-00495-z","url":null,"abstract":"We conduct a non-asymptotic study of the Cross-Validation (CV) estimate of the generalization risk for learning algorithms dedicated to extreme regions of the covariates space. In this context which has recently been analysed from an Extreme Value Analysis perspective, the risk function measures the algorithm’s error given that the norm of the input exceeds a high quantile. The main challenge within this framework is the negligible size of the extreme training sample with respect to the full sample size and the necessity to re-scale the risk function by a probability tending to zero. We open the road to a finite sample understanding of CV for extreme values by establishing two new results: an exponential probability bound on the K-fold CV error and a polynomial probability bound on the leave-p-out CV. Our bounds are sharp in the sense that they match state-of-the-art guarantees for standard CV estimates while extending them to encompass a conditioning event of small probability. We illustrate the significance of our results regarding high dimensional classification in extreme regions via a Lasso-type logistic regression algorithm. The tightness of our bounds is investigated in numerical experiments.","PeriodicalId":49274,"journal":{"name":"Extremes","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142182396","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 Gaussian triangular arrays in the case of strong dependence 关于强依赖情况下的高斯三角形阵列

IF 1.3 3区数学

Extremes Pub Date : 2024-09-03 DOI: 10.1007/s10687-024-00491-3

Evgeniy Savinov

引用次数: 0

Estimation of marginal excess moments for Weibull-type distributions 魏布尔型分布的边际超额矩估计

IF 1.3 3区数学

Extremes Pub Date : 2024-09-02 DOI: 10.1007/s10687-024-00494-0

Yuri Goegebeur, Armelle Guillou, Jing Qin

引用次数: 0

Probability of entering an orthant by correlated fractional Brownian motion with drift: exact asymptotics 带漂移的相关分数布朗运动进入正交的概率：精确渐近学