论文标题
在分段线性下进行变更点检测的移动总和程序
Moving sum procedure for change point detection under piecewise linearity
论文作者
论文摘要
我们提出了一个计算和统计上有效的程序，用于在分段线性下分割单变量数据。提出的移动总和（MOSUM）方法可检测到基础信号不连续跳跃和/或斜率变化的多个变更点。从理论上讲，它在给定的显着性水平上控制家庭的错误率，并在多个变更点检测中达到一致性，并在信号分子线性和连续的弱假设下，允许串行依赖性和繁重尾巴的弱假设下，在多个变化点检测中达到一致性。从计算上讲，Mosum过程的复杂性为$ O（N）$，结合其在模拟数据集上的良好性能，与现有方法相比，它具有很有吸引力。我们进一步证明了它在滚动元素带有预后的真实数据示例上的良好性能。
We propose a computationally and statistically efficient procedure for segmenting univariate data under piecewise linearity. The proposed moving sum (MOSUM) methodology detects multiple change points where the underlying signal undergoes discontinuous jumps and/or slope changes. Theoretically, it controls the family-wise error rate at a given significance level asymptotically and achieves consistency in multiple change point detection, as well as matching the minimax optimal rate of estimation when the signal is piecewise linear and continuous, all under weak assumptions permitting serial dependence and heavy-tailedness. Computationally, the complexity of the MOSUM procedure is $O(n)$ which, combined with its good performance on simulated datasets, making it highly attractive in comparison with the existing methods. We further demonstrate its good performance on a real data example on rolling element-bearing prognostics.
