基于BCUSUM的多参数变点估计  

BCUSUM-based Multi-parameter Change Point Estimation

作　　者：王继梅 胡尧 Wang Jimei;Hu Yao(School of Mathematics and Statistics,Guizhou University,Guiyang 550025,China;State Key Laboratory of Public Big Data,Guizhou University,Guiyang 550025,China)

机构地区：[1]贵州大学数学与统计学院,贵阳550025 [2]贵州大学公共大数据国家重点实验室,贵阳550025

出　　处：《统计与决策》2024年第9期61-66,共6页Statistics & Decision

基　　金：国家自然科学基金资助项目(12161016,11661018);贵州省数据驱动建模学习与优化创新团队项目(黔科合平台人才[2020]5016号);贵州省科技计划项目(黔科合基础-ZK[2024]一般082)。

摘　　要：文章基于递归残差的逆序特征和隔离检测研究了回归模型多参数变点的检测方法。首先,构建带有变点的回归模型,考虑到多元正向CUSUM检验能防止协变量均值与偏移量正交时损失功效,但其变点检测效果并不理想的情况,引入修正的检验统计量BCUSUM。其次,结合快速高效的隔离检测技术,提出MCPDP算法用于估计变点数目及位置。最后,模拟结果表明,所提出的方法能较好地控制检验水平,有更高的功效;评价结果显示,MCPDP算法在变点估计性能方面表现较优;实例分析表明,交通流变点符合实际交通情况,验证了该方法的有效性,且所构建的模型可以作为交通参数确定性经验关系的一种修正。This paper investigates the detection method of multi-parameter change points in regression model based on the inverse order characteristics of recursive residuals and isolate-detect.Firstly,the regression model with change points is constructed.In view of the fact that the multivariate forward CUSUM test prevents the loss of power when the mean of the covariates is orthogonal to the offset,but that its change point detection effect is not ideal,the modified test statistic BCUSUM(Backward Cumulative Sum)is introduced.Secondly,with the fast and efficient isolate-detect technology combined,a MCPDP(Multiple Change Points Detection of Parameter)algorithm is proposed to estimate the number and corresponding positions of change points.Finally,the simulation results show that the proposed method can control the test level well and has higher power.The evaluation results show that the MCPDP algorithm has better performance of change point estimation.The case analysis shows that the traffic flow change points are consistent with the actual traffic situations,which verifies the effectiveness of the method.The model constructed in this paper can be used as a modification of the deterministic empirical relationship of traffic parameters.

关 键 词：多参数变点 逆向累积和 隔离检测 递归残差 

分 类 号：O212.1[理学—概率论与数理统计]