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Testing mean changes by maximal ratio statistics 用最大比值统计检验平均值变化
IF 1.3 3区 数学
Extremes Pub Date : 2021-11-17 DOI: 10.1007/s10687-021-00423-5
Gudan, Jovita, Račkauskas, Alfredas, Suquet, Charles
{"title":"Testing mean changes by maximal ratio statistics","authors":"Gudan, Jovita, Račkauskas, Alfredas, Suquet, Charles","doi":"10.1007/s10687-021-00423-5","DOIUrl":"https://doi.org/10.1007/s10687-021-00423-5","url":null,"abstract":"<p>We propose a new test statistic <span>(mathrm {MR}_{gamma ,n})</span> for detecting a changed segment in the mean, at unknown dates, in a regularly varying sample. Our model supports several alternatives of shifts in the mean, including one change point, constant, epidemic and linear form of a change. Our aim is to detect a short length changed segment <span>(ell ^{*})</span>, assuming <span>(ell^*/n)</span> to be small as the sample size <i>n</i> is large. <span>(mathrm {MR}_{gamma ,n})</span> is built by taking maximal ratios of weighted moving sums statistics of four sub-samples. An important feature of <span>(mathrm {MR}_{gamma ,n})</span> is to be scale free. We obtain the limiting distribution of ratio statistics under the null hypothesis as well as their consistency under the alternative. These results are extended from i.i.d. samples under <span>(H_0)</span> to some dependent samples. To supplement theoretical results, empirical illustrations are provided by generating samples from symmetrized Pareto and Log-Gamma distributions.</p>","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"29 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138537968","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
Extremal lifetimes of persistent cycles 持久周期的极限生命周期
IF 1.3 3区 数学
Extremes Pub Date : 2021-10-30 DOI: 10.1007/s10687-021-00430-6
Chenavier, Nicolas, Hirsch, Christian
{"title":"Extremal lifetimes of persistent cycles","authors":"Chenavier, Nicolas, Hirsch, Christian","doi":"10.1007/s10687-021-00430-6","DOIUrl":"https://doi.org/10.1007/s10687-021-00430-6","url":null,"abstract":"<p>Persistent homology captures the appearances and disappearances of topological features such as loops and cavities when growing disks centered at a Poisson point process. We study extreme values for the lifetimes of features dying in bounded components and with birth resp. death time bounded away from the threshold for continuum percolation and the coexistence region. First, we describe the scaling of the minimal lifetimes for general feature dimensions, and of the maximal lifetimes for cavities in the Čech filtration. Then, we proceed to a more refined analysis and establish Poisson approximation for large lifetimes of cavities and for small lifetimes of loops. Finally, we also study the scaling of minimal lifetimes in the Vietoris-Rips setting and point to a surprising difference to the Čech filtration.</p>","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"48 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138537937","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
Running minimum in the best-choice problem 在最佳选择问题中求最小值
IF 1.3 3区 数学
Extremes Pub Date : 2021-10-11 DOI: 10.1007/s10687-022-00457-3
A. Gnedin, Patryk Koziel, M. Sułkowska
{"title":"Running minimum in the best-choice problem","authors":"A. Gnedin, Patryk Koziel, M. Sułkowska","doi":"10.1007/s10687-022-00457-3","DOIUrl":"https://doi.org/10.1007/s10687-022-00457-3","url":null,"abstract":"","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"26 1","pages":"157-182"},"PeriodicalIF":1.3,"publicationDate":"2021-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46063641","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 censored and uncensored lifetimes in survival data 生存数据中被删减和未删减寿命的极值
IF 1.3 3区 数学
Extremes Pub Date : 2021-10-09 DOI: 10.1007/s10687-021-00426-2
Maller, Ross, Resnick, Sidney
{"title":"Extremes of censored and uncensored lifetimes in survival data","authors":"Maller, Ross, Resnick, Sidney","doi":"10.1007/s10687-021-00426-2","DOIUrl":"https://doi.org/10.1007/s10687-021-00426-2","url":null,"abstract":"<p>We consider a random censoring model for survival analysis, allowing the possibility that only a proportion of individuals in the population are susceptible to death or failure, and the remainder are immune or cured. Susceptibles suffer the event under study eventually, but the time at which this occurs may not be observed due to censoring. Immune individuals have infinite lifetimes which are always censored in the sample. Assuming that the distribution of the susceptibles’ lifetimes as well as the censoring distribution have infinite right endpoints and are in the domain of attraction of the Gumbel distribution, we obtain asymptotic distributions, as sample size tends to infinity, of statistics relevant to testing for the possible existence of immunes in the population.</p>","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"196 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138537945","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
Pandemic-type failures in multivariate Brownian risk models 多变量布朗风险模型中的大流行型失效
IF 1.3 3区 数学
Extremes Pub Date : 2021-09-22 DOI: 10.1007/s10687-021-00424-4
Dȩbicki, Krzysztof, Hashorva, Enkelejd, Kriukov, Nikolai
{"title":"Pandemic-type failures in multivariate Brownian risk models","authors":"Dȩbicki, Krzysztof, Hashorva, Enkelejd, Kriukov, Nikolai","doi":"10.1007/s10687-021-00424-4","DOIUrl":"https://doi.org/10.1007/s10687-021-00424-4","url":null,"abstract":"<p>Modelling of multiple simultaneous failures in insurance, finance and other areas of applied probability is important especially from the point of view of pandemic-type events. A benchmark limiting model for the analysis of multiple failures is the classical <i>d</i>-dimensional Brownian risk model (Brm), see Delsing et al. (Methodol. Comput. Appl. Probab. <b>22</b>(3), 927–948 2020). From both theoretical and practical point of view, of interest is the calculation of the probability of multiple simultaneous failures in a given time horizon. The main findings of this contribution concern the approximation of the probability that at least <i>k</i> out of <i>d</i> components of Brm fail simultaneously. We derive both sharp bounds and asymptotic approximations of the probability of interest for the finite and the infinite time horizon. Our results extend previous findings of Dȩbicki et al. (J. Appl. Probab. <b>57</b>(2), 597–612 2020) and Dȩbicki et al. (Stoch. Proc. Appl. <b>128</b>(12), 4171–4206 2018).</p>","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"65 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138537969","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: 3
Choquet random sup-measures with aggregations 带聚合的随机超测度
IF 1.3 3区 数学
Extremes Pub Date : 2021-09-20 DOI: 10.1007/s10687-021-00425-3
Wang, Yizao
{"title":"Choquet random sup-measures with aggregations","authors":"Wang, Yizao","doi":"10.1007/s10687-021-00425-3","DOIUrl":"https://doi.org/10.1007/s10687-021-00425-3","url":null,"abstract":"<p>A variation of Choquet random sup-measures is introduced. These random sup-measures are shown to arise as the scaling limits of empirical random sup-measures of a general aggregated model. Because of the aggregations, the finite-dimensional distributions of introduced random sup-measures do not necessarily have classical extreme-value distributions. Examples include the recently introduced stable-regenerative random sup-measures as a special case.</p>","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"19 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138537971","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: 3
Branching processes with immigration in atypical random environment 非典型随机环境下具有迁移的分支过程
IF 1.3 3区 数学
Extremes Pub Date : 2021-09-20 DOI: 10.1007/s10687-021-00427-1
Foss, Sergey, Korshunov, Dmitry, Palmowski, Zbigniew
{"title":"Branching processes with immigration in atypical random environment","authors":"Foss, Sergey, Korshunov, Dmitry, Palmowski, Zbigniew","doi":"10.1007/s10687-021-00427-1","DOIUrl":"https://doi.org/10.1007/s10687-021-00427-1","url":null,"abstract":"<p>Motivated by a seminal paper of Kesten et al. (<i>Ann. Probab.</i>, <i>3(1)</i>, 1–31, 1975) we consider a branching process with a conditional geometric offspring distribution with i.i.d. random environmental parameters <i>A</i><sub><i>n</i></sub>, <i>n</i> ≥ 1 and with one immigrant in each generation. In contrast to above mentioned paper we assume that the environment is long-tailed, that is that the distribution <i>F</i> of <span>(xi _{n}:=log ((1-A_{n})/A_{n}))</span> is long-tailed. We prove that although the offspring distribution is light-tailed, the environment itself can produce extremely heavy tails of the distribution of the population size in the <i>n</i> th generation which becomes even heavier with increase of <i>n</i>. More precisely, we prove that, for all <i>n</i>, the distribution tail <span>(mathbb {P}(Z_{n} ge m))</span> of the <i>n</i> th population size <i>Z</i><sub><i>n</i></sub> is asymptotically equivalent to <span>(noverline F(log m))</span> as <i>m</i> grows. In this way we generalise Bhattacharya and Palmowski (<i>Stat. Probab. Lett.</i>, <i>154</i>, 108550, 2019) who proved this result in the case <i>n</i> = 1 for regularly varying environment <i>F</i> with parameter <i>α</i> &gt; 1. Further, for a subcritical branching process with subexponentially distributed <i>ξ</i><sub><i>n</i></sub>, we provide the asymptotics for the distribution tail <span>(mathbb {P}(Z_{n}&gt;m))</span> which are valid uniformly for all <i>n</i>, and also for the stationary tail distribution. Then we establish the “principle of a single atypical environment” which says that the main cause for the number of particles to be large is the presence of a single very small environmental parameter <i>A</i><sub><i>k</i></sub>.</p>","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"34 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138537967","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 subexponential Lévy-driven random fields in the Gumbel domain of attraction 甘贝尔引力域中亚指数lsamv驱动随机场的极值
IF 1.3 3区 数学
Extremes Pub Date : 2021-09-11 DOI: 10.1007/s10687-021-00428-0
Mads Stehr, Anders Rønn-Nielsen
{"title":"Extremes of subexponential Lévy-driven random fields in the Gumbel domain of attraction","authors":"Mads Stehr, Anders Rønn-Nielsen","doi":"10.1007/s10687-021-00428-0","DOIUrl":"https://doi.org/10.1007/s10687-021-00428-0","url":null,"abstract":"","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"25 1","pages":"79 - 105"},"PeriodicalIF":1.3,"publicationDate":"2021-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52394337","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: 2
The asymptotic distribution of the condition number for random circulant matrices 随机循环矩阵条件数的渐近分布
IF 1.3 3区 数学
Extremes Pub Date : 2021-09-06 DOI: 10.1007/s10687-022-00442-w
G. Barrera, Paulo Manrique-Mirón
{"title":"The asymptotic distribution of the condition number for random circulant matrices","authors":"G. Barrera, Paulo Manrique-Mirón","doi":"10.1007/s10687-022-00442-w","DOIUrl":"https://doi.org/10.1007/s10687-022-00442-w","url":null,"abstract":"","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"25 1","pages":"567 - 594"},"PeriodicalIF":1.3,"publicationDate":"2021-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43233925","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: 2
Asymptotic dependence of in- and out-degrees in a preferential attachment model with reciprocity 具有互惠的优先依恋模型中进出度的渐近依赖
IF 1.3 3区 数学
Extremes Pub Date : 2021-08-06 DOI: 10.1007/s10687-022-00439-5
Tiandong Wang, S. Resnick
{"title":"Asymptotic dependence of in- and out-degrees in a preferential attachment model with reciprocity","authors":"Tiandong Wang, S. Resnick","doi":"10.1007/s10687-022-00439-5","DOIUrl":"https://doi.org/10.1007/s10687-022-00439-5","url":null,"abstract":"","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"25 1","pages":"417 - 450"},"PeriodicalIF":1.3,"publicationDate":"2021-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42474995","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: 7
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