基于BCUSUM的多参数变点估计

BCUSUM-based Multi-parameter Change Point Estimation

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.