广义Pareto分布变点检测似然比模型  

A Likelihood Ratio Model for Change Point Detection of Generalized Pareto Distribution

作　　者：胡尧 谌业文[3] HU YAO;CHEN YEWEN(School of Mathematics and Statistics,Guizhou University,Guiyang 550025,China;Guizhou Provincial Key Laboratory of Public Big Data,Guizhou University,Guiyang 550025,China;School of Mathematics,Sun Yat-sen University,Guangzhou 510000,China)

机构地区：[1]贵州大学数学与统计学院,贵阳550025 [2]贵州大学贵州省公共大数据重点实验室,贵阳550025 [3]中山大学数学学院,广州510000

出　　处：《应用数学学报》2021年第4期553-573,共21页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11661018);贵州省科技计划项目(黔科合平台人才[2017]5788号);贵州省数据驱动建模学习与优化创新团队(黔科合平台人才[2020]5016号);全国统计科学研究(2014LZ46);贵州省自然科学基金(黔科合J字[2014]2058号)资助项目。

摘　　要：为检测极端事件的状态变化,基于似然比方法研究了广义Pareto分布(Generalized Pareto Distribution,GPD)变点检测模型.考虑三参数GPD变点的检验问题,提出了最大似然比检验统计量.通过证明参数变换后GPD的对数似然和检验统计量的一系列极限性质,得到了检验统计量的渐近分布.通过模拟研究,对该方法的有限样本性质进行了评价,实例分析也验证了该方法的可行性.To detect state changes in extreme events,the generalized Pareto distribution(GPD)change point detection model was studied based on likelihood ratio method.This paper considered the testing problem of the GPD change point with three parameters,and proposed maximization likelihood ratio test statistics.The asymptotic distribution of test statistic was obtained by proving a series of limit properties of the log-likelihood of GPD after parameter transformation and the test statistic.We evaluated the finite sample properties of the proposed method through simulation studies.The case study also verified the feasibility of the proposed method.

关 键 词：广义PARETO分布 参数变点 变点检测 似然比检验统计量 交通流 

分 类 号：O212.1[理学—概率论与数理统计]