带未知多个变点的均值突变模型的多阶段估计  

Multi-stage Estimation for Mean-shift Model with the Unknown Number of Change-points

作　　者：夏志明[1] 赵文芝[2] XIA ZHIMING;ZHAO WENZHI(School of Mathematics, Northwest University, Xi＇an 710027, China;School of Science, Xi＇an Polytechnic University, Xi＇an 710048, China)

机构地区：[1]西北大学统计系,西安710127 [2]西安工程大学理学院,西安710048

出　　处：《应用数学学报》2017年第6期931-952,共22页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金面上项目(11771353);国家自然科学基金青年项目(11201372);教育部人文社科一般项目(10YJC910007)资助

摘　　要：本文基于局部比较法,提出了带未知多个变点的均值突变模型中变点个数与变点位置的多步估计.首先估计出可能变点位置的报警区间序列;然后根据这些报警区间初步估计出变点个数及变点位置;最后对虚假变点进行删除确定最终变点个数及变点位置.理论结果表明:几乎必然的,当n充分大时,变点个数估计将严格等于变点个数真值,所得最终报警区间将严格包含变点真值;变点估计量具有强相合性.随机模拟结果表明,多步估计在不同条件下均能准确估计变点个数和变点位置.In this paper, based on local comparison, a multi-stage estimation method for the number and the location of change-points is proposed in mean-shift model with unknown multiple change points. First, the alarm interval sequence of possible change-point positions are estimated; then the number and the location of change-points are preliminarily estimated according to the alarm intervals; finally, the false change-points are deleted to determine the final number and the location of change-points. The theoretical results show that almost surely when the n is sufficiently large, the number of change points will be exactly equal to the true number of the change points, and the final alarm interval will strictly contain all true change-points. The estimator has strong consistency. The simulation results show that the multi-stage estimation can accurately estimate the number and the location of change-points under different conditions.

关 键 词：均值突变模型 局部比较法 变点 阈值 

分 类 号：O212.1[理学—概率论与数理统计]