越来越多的证据表明，仅考虑单一变点的模型具有很大的局限性。在实际应用中，特别是针对长时间序列的分析，这些序列往往存在多个变点。而且为解决单变点问题而设计的方法，在尝试检测多个变点时难以取得理想的效果。鉴于此，本文将采用M估计方法，针对厚尾序列均值多变点检验问题进行分析，包括线下检验与在线监测两大核心内容，具体内容如下：
      现有的关于厚尾序列均值多变点检验的研究其统计量主要依赖最小二乘估计方法，但对异常值非常敏感，特别是在厚尾情形下性能显著降低。鉴于M估计的稳健性，本文构造了相应的比值检验统计量，并通过隔离检测方法检验厚尾序列均值多变点。不仅得到在原假设下基于M估计的比值型检验统计量的渐近分布，并在备择假设下给出相合性。此外，为了估计变点，提出了变点估计方法以确定变点位置，并进一步证明了其一致性以及收敛速度。仿真结果表明，与最小二乘估计相比，基于M估计的比率型检验对经验水平没有显著影响，并且经验势显著提高，特别是在厚尾下更具鲁棒性。通过采用隔离分割的方法，能够有效地解决数据中存在多个变点的问题，并且与现有方法相比，提高了估计精度。最后，选取两组数据说明了本文方法的有效性和实用性。
       鉴于线下检验方法在应对在线监测时失效的问题，并充分考虑数据的动态变化过程，进一步探索在线监测方法。在充分利用M估计优势基础上，结合ID隔离的思想，提出了一种改进的基于M估计的在线监测统计量。通过采用滑动的方式，旨在解决厚尾情形下关于均值多变点的监测问题。经过理论推导证明了在原假设下的渐近分布同样为布朗运动的泛函，同时在备择假设下证明了一致性。通过数值模拟分析，发现相比于最小二乘估计，基于M估计的统计量不仅有较高的经验势，而且其平均运行长度更短，这意味着可以在较短的运行长度内有效地监测出均值多变点。两组数据验证了本文所提的在线监测方法的有效性。

There is growing evidence that models that consider only a single change point have significant limitations. In practice, this is especially true for analyses of long time series, which often have multiple change points. Moreover, methods designed to address the single change point problem struggle to achieve the desired results when attempting to detect multiple change points. In view of this, this thesis will adopt the M estimation method to analyse the problem of multiple change point testing for the mean of heavy-tailed sequences, including the two core contents of offline testing and online monitoring, as follows:
Existing studies on the test for multiple change points in the mean of heavy-tailed sequences have statistics that rely mainly on the least squares estimation method, but it is very sensitive to outliers, and its performance is significantly degraded especially in the heavy-tailed case. In view of the robustness of M estimation, this thesis constructs the corresponding ratio test statistic and tests the heavy-tailed sequence mean multiple change points by isolation detection method. Not only the asymptotic distribution of the ratio-type test statistic based on M estimation is obtained under the original hypothesis, but also the collinearity is given under the alternative hypothesis. In addition, to estimate the change points, the change point estimation method is proposed to determine the change point locations and further proves the consistency as well as the convergence speed. Simulation results show that the Ratio test based on M-estimation has no significant effect on the empirical level and the empirical power is significantly higher and more robust especially under heavy-tailed compared to the least squares estimation. By using the method of isolated segmentation, the problem of multiple change points in the data can be effectively solved and the estimation accuracy is improved compared with the existing methods. Finally, two sets of data are selected to illustrate the effectiveness and practicality of the method in this thesis.
In view of the failure of offline test methods in coping with online monitoring, and with full consideration of the dynamic process of data change, online monitoring methods are further explored. On the basis of making full use of the advantages of M-estimation and combining the idea of ID isolation, an improved online monitoring statistic based on M-estimation is proposed. By adopting a sliding approach, it aims to solve the monitoring problem about the mean multi-variable points in the heavy-tailed case. After theoretical derivation, it is proved that the asymptotic distribution under the null hypothesis is also a generalised function of Brownian motion, while consistency is proved under the alternative hypothesis. Through numerical simulation analysis, it is found that compared with the least squares estimation, the statistics based on M-estimation not only have higher empirical powers, but also have shorter average run lengths, which implies that the mean multiple change points can be efficiently monitored in a shorter run length. The two sets of data validate the effectiveness of the online monitoring method proposed in this thesis. 

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