In this paper, we propose a new generic method for detecting the number and locations of structural breaks or change points in piecewise linear models under stationary Gaussian noise. Our method transforms the change point detection problem into identifying local extrema (local maxima and local minima) through kernel smoothing and differentiation of the data sequence. By computing p-values for all local extrema based on peak height distributions of smooth Gaussian processes, we utilize the Benjamini-Hochberg procedure to identify significant local extrema as the detected change points. Our method can distinguish between two types of change points: continuous breaks (Type I) and jumps (Type II). We study three scenarios of piecewise linear signals, namely pure Type I, pure Type II and a mixture of Type I and Type II change points. The results demonstrate that our proposed method ensures asymptotic control of the False Discover Rate (FDR) and power consistency, as sequence length, slope changes, and jump size increase. Furthermore, compared to traditional change point detection methods based on recursive segmentation, our approach only requires a single test for all candidate local extrema, thereby achieving the smallest computational complexity proportionate to the data sequence length. Additionally, numerical studies illustrate that our method maintains FDR control and power consistency, even in non-asymptotic cases when the size of slope changes or jumps is not large. We have implemented our method in the R package "dSTEM" (available from https://cran.r-project.org/web/packages/dSTEM).

翻译：本文提出一种新的通用方法，用于在平稳高斯噪声条件下检测分段线性模型中结构断点或变化点的数量与位置。该方法通过核平滑与数据序列微分，将变化点检测问题转化为识别局部极值（局部极大值与局部极小值）。基于光滑高斯过程峰值高度分布计算所有局部极值的p值后，利用Benjamini-Hochberg程序识别显著局部极值作为检测到的变化点。本方法可区分两类变化点：连续型断点（类型I）与跳跃型断点（类型II）。我们研究了三种分段线性信号场景，即纯类型I、纯类型II以及类型I与类型II混合的变化点。结果表明，随着序列长度、斜率变化幅度与跳跃幅度的增加，所提方法能确保错误发现率（FDR）的渐近控制与检验功效一致性。此外，与基于递归分割的传统变化点检测方法相比，本方法仅需对所有候选局部极值进行一次检验，从而实现了与数据序列长度成比例的最小计算复杂度。数值实验进一步表明，即使斜率变化或跳跃幅度不大的非渐近情形下，该方法仍能维持FDR控制与功效一致性。我们已将所提方法实现于R包"dSTEM"中（可从https://cran.r-project.org/web/packages/dSTEM获取）。