基于MOSUM的多重滤波变点检测研究

多时间尺度的变点问题一直是质量控制中的热点研究对象。基于移动和统计量(MOSUM),提出了一种多重过滤检验方法(MFT),以检验均值不变的零假设或存在均值变点的备择假设。首先,为使方法具有实用性和一般性,构建均值变点模型,并假定分布假设较弱。其次,由于单一窗宽对变点检测的局限性,构造了一个弱收敛到一个布朗运动相关的函数的MOSUM统计量,进而应用多个窗宽下MOSUM过程进行多变点检测。最后,为使得MFT方法不受其它分布参数变化影响,对模型均值外的参数变化作了鲁棒性检验。经模拟研究和实证分析表明,MFT方法的估计精度和准确度比一般方法更具优势和实效性。

Research on Multi-filter Change Point Detection Based on MOSUM

The multi-time-scale change point problem has always been a popular research object in quality control.Based on the moving sum statistics(MOSUM),a multiple filtering test method(MFT),is proposed to test the zero hypothesis with constant mean or the alternative hypothesis with the existence of mean change point.First of all,for the practicability and generality of the method,the mean change point model is constructed,and the distribution assumption is weak.Secondly,due to the limitation of single window width for variable point detection,a MOSUM statistic which weakly converges to a Brownian motion dependent function is constructed,and then the MOSUM process with multiple window widths is applied to multi-variable point detection.Finally,in order to make the MFT method not affected by the changes of other distributed parameters,the robustness of the parameter changes outside the mean value of the model is tested.The simulation and empirical analysis show that the estimation accuracy of MFT method are more superior and effective.