多元正态向量均值变点在线监测

发布时间：2017-12-31 18:01

本文关键词：多元正态向量均值变点在线监测　出处：《山西大学》2015年硕士论文　论文类型：学位论文

【摘要】：变点问题是自上世纪70年代以来的热门课题。最初应用在工业质量控制中,后来又逐渐渗透到经济、金融、医学、气候分析等诸多领域。近三十年来,随着统计学者在这一领域的投入,目前已有大量关于变点理论和应用方面的学术论文。已有论文中关于位置参数变点的研究有很多,尤其是关于均值变点的研究,而关于多元均值变点的研究则比较少。本文主要研究了正态多元向量均值变点监测问题。文中我们利用残差累积和与递归残差累积和构造统计量,在原假设下得到了监测统计量的渐近分布,在备择假设下证明了该监测统计量的一致性,并模拟得到统计量的临界值。数字模拟实验与生产实例表明,当变点的位置靠前时该统计量有较高的势,但是当变点的位置靠后时并不总能及时监测到变点。因此,我们采用引入窗宽参数的方法,对统计量进行修正,使得对位置靠后的变点能及时预警。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。最后的生产实例也能说明该方法的实用性和有效性。
[Abstract]:The change point problem is a hot topic since the last century since 70s. The initial application in industrial quality control, then gradually penetrated into the economic, financial, medical, climate analysis and other areas. In the past thirty years, with statistical researchers in this field, there are a large amount of change point theory and Application the academic papers have studied in this thesis. A variable position parameters are many, especially the research on the mean change point, and the research on multivariate mean change point is relatively small. This paper mainly studies the normal vector of mean change point detection problem. In this paper, we make use of the residual accumulation and accumulation of recursive residuals and the structure of the statistic, under the null hypothesis and obtain the asymptotic distribution of the monitoring statistic, the consistency of the monitoring statistic is proved under the alternative hypothesis, and simulate the critical value of statistics. The digital simulation experiment with the students Production examples show that when the change point position in front of the statistics have high potential, but when the change point position back does not always detect the change point. Therefore, we proposed using window width parameter, to statistic correction, the change point position on the timely warning simulation. The results show that the bandwidth parameter can indeed improve the monitoring statistics, at the same time can reduce the average run length. The final production examples can illustrate the practicability and effectiveness of the method.

【学位授予单位】：山西大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O212.4

【共引文献】