Monitoring Change In The Mean Vector Of Multivariate Normal Distribution

Change point problem attracts increasing attention since the 1970s. It has originally arisen in the context of industrial quality control, and then filtered through economics, finance, medicine, climate analysis and many other fields. In the last three decades, as the considerable efforts of the statistics in this field, there are a lot of theories and applied achievements. However, most of literatures are focus on the study of location parameters change point, especially on the study of the mean change point, the literatures about the multivariate mean change point are relatively much less. Considering this, we proposed two monitoring procedures in the mean vector of normal distribution in this thesis.The monitoring statistics were constructed by employing the CUSUM of residuals and recursive residuals. Under the null hypothesis we derive the limiting distribution, and tab-ulate some critical values, we also prove its consistency under the alternative hypothesis. Simulations and production instance indicate that the procedure has high power for changes occur at the early stage of monitoring, and is insensitive when change point occurs after a relative longer monitoring time. Therefore, we adopt the method by introducing bandwidth parameter to modify the statistics. Simulations indicate that introducing a bandwidth pa-rameter can improve the power of the monitoring statistics and can reduce the average run length, and the practical production illustrates the practicability and the effectiveness of the approach.