论文标题
检测多个变更点:脉冲标准
Detecting multiple change points: a PULSE criterion
论文作者
论文摘要
在此描述的研究中,研究了一系列观测的检测平均值和方差的变化点。随着样本量为无穷大,变化点的数量可以在一定速率上发散。为此,我们定义了基于MOSUM的目标函数。与所有现有基于MOSUM的方法不同,新型目标函数在含义上显示出有用的``脉冲”模式了:在人群级别上,任何变化点的价值加上移动平均线的段的2次,在局部最小趋向于当地的最小值之后,通过到零的最大值,最大程度地趋于无限。在某种意义上,由于其可视化的性质,在某种程度上,这些位置比现有方法相对容易地识别。
The research described herewith investigates detecting change points of means and of variances in a sequence of observations. The number of change points can be divergent at certain rate as the sample size goes to infinity. We define a MOSUM-based objective function for this purpose. Unlike all existing MOSUM-based methods, the novel objective function exhibits an useful ``PULSE" pattern near change points in the sense: at the population level, the value at any change point plus 2 times of the segment length of the moving average attains a local minimum tending to zero following by a local maximum going to infinity. This feature provides an efficient way to simultaneously identify all change points at the sample level. In theory, the number of change points can be consistently estimated and the locations can also be consistently estimated in a certain sense. Further, because of its visualization nature, in practice, the locations can be relatively more easily identified by plots than existing methods in the literature. The method can also handle the case in which the signals of some change points are very weak in the sense that those changes go to zero. Further, the computational cost is very inexpensive. The numerical studies we conduct validate its good performance.