基于二分法的空间函数型数据变点检测  

Changepoint detection of the spatial functional data based on binary segmentation

作　　者：李云霞 张帅 LI Yun-xia;ZHANG Shuai(School of Data Sciences,Zhejiang University of Finance and Economic,Hangzhou 310018,China)

机构地区：[1]浙江财经大学数据科学学院,浙江杭州310018

出　　处：《高校应用数学学报(A辑)》2025年第1期1-14,共14页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家社会科学基金(23BTJ048)。

摘　　要：针对具有空间特征的函数型数据,在经典累积和(Cumulative Sum,CUSUM)统计量和二分法(Binary Segmentation,BS)的动态规划变点检测方法基础上,提出空间函数型二分法(Spatial Functional Binary Segmentation,SFBS)以及相应函数型CUSUM统计量-空间累积和统计量(Spatial Cumulative Sum,SCUSUM),并证明其渐近分布.该方法将检测数据扩展至具有更高维度信息的空间函数型数据,以此检测空间中的变点位置.SFBS方法主要将空间数据按照与各空间坐标轴平行的方向进行分割,将原本的空间划分为更小的子空间,并且在划分好的子空间上逐一利用SCUSUM统计量与BS方法进行结构变点的检测,最终获得精确的检测结果.同时,对提出的方法进行模拟,最后将该方法应用于气温数据进行实证分析.In this paper,based on the classical Cumulative Sum(CUSUM)statistic and the dy-namic programming change detection method called Binary Segmentation(BS),the Spatial Functional Binary Segmentation(SFBS)and the corresponding functional CUSUM statistic,Spatial Cumulative Sum(SCUSUM),are proposed,and the asymptotic distribution of the statistic is proved.This method studies the spatial functional data with high-dimensional information,which can detect changepoints in space.The SFBS method mainly divides the spatial data in the direction parallel to each spatial coordinate axis to get smaller subspaces of original space,using the SCUSUM statistic and BS method to detect structural changepoints one by one on the divided subspace.Finally,accurate results of changepoints are achieved.Simultaneously,the method is simulated and applied to the temperature data for analysis.

关 键 词：CUSUM 动态规划 函数型数据 空间二分法 

分 类 号：O212[理学—概率论与数理统计]