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.

翻译：我们提出一种在分段线性假设下对单变量数据进行分割的高计算效率与统计效率方法。所提出的移动求和（MOSUM）方法能检测潜在信号发生不连续跳跃和/或斜率变化时的多个变点。在理论上，该方法能在给定显著性水平下渐近控制族系误差率，实现多个变点检测的一致性，并在信号为分段线性且连续的情况下达到极小化最优估计速率——所有结论均在允许序列依赖性和重尾性的宽松假设下成立。在计算方面，MOSUM过程的复杂度为$O(n)$，结合其在模拟数据集上的良好表现，使其与现有方法相比具有高度吸引力。我们进一步通过滚动轴承故障预测的实际数据案例展示了其优异性能。