多元正态向量变点在线监测  

Monitoring Change in the Mean Vector of Multivariate Normal Distribution

作　　者：刘维奇[1,2] 刘晋芳[2] 秦瑞兵[2] 

机构地区：[1]山西大学管理与决策研究所,山西太原030006 [2]山西大学数学科学学院,山西太原030006

出　　处：《山西大学学报（自然科学版）》2015年第3期469-475,共7页Journal of Shanxi University(Natural Science Edition)

基　　金：教育部人文社科研究项目(14JA790034);国家自然科学基金数学天元基金(11226217)

摘　　要：针对多元时间序列均值向量变点发生时刻靠后的情况,文章通过采用引入窗宽参数h的方法,构造残差累积和统计量,使得多元正态均值过程变点位置靠后时能尽早提出预警。在原假设下得到了监测统计量的渐近分布,并在备择假设下证明了该监测统计量的一致性。模拟结果表明引入窗宽参数确实能够提高监测统计量的势,同时能减小平均运行长度。最后将本文的方法应用到生产实例中,表明该方法具有一定的实践性和有效性。For the change point occurred at the last stage of the mean vector of multivariate time series,we proposed a monitoring scheme by using the CUSUM of residuals to quickly detect it in the mean vector of independent multivariate process by introducing a bandwidth parameter.The null distributions of the monitoring statistics were obtained,and the consistency of the statistics under the alternative hypothesis was also proved.The simulations indicate that introducing a bandwidth parameter can improve the power of the monitoring statistics and can reduce the average run length.Moreover,we applied the procedures to a practical production which illustrates the practicability and the effectiveness of the approach.

关 键 词：多元正态 变点监测 窗宽参数 平均运行长度 

分 类 号：O212[理学—概率论与数理统计]