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：本文提出了一种新的通用方法，用于在平稳高斯噪声下检测分段线性模型中结构突变或变点的数量及位置。我们的方法通过核平滑与数据序列微分，将变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）。基于平滑高斯过程的峰值高度分布计算所有局部极值的p值后，利用Benjamini-Hochberg过程筛选出作为检测变点的显著局部极值。该方法能区分两类变点：连续突变（I型）与跳跃突变（II型）。我们研究了三种分段线性信号场景——纯I型、纯II型及I型与II型混合变点。结果表明，随着序列长度、斜率变化幅度及跳跃幅度的增加，所提方法能保证错误发现率（FDR）的渐近控制与检验势一致性。相较于基于递归分割的传统变点检测方法，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正比的最小计算复杂度。此外，数值实验表明，即使斜率变化或跳跃幅度不大的非渐近情形下，方法仍能维持FDR控制与检验势一致性。该方法已在R包"dSTEM"中实现（可从https://cran.r-project.org/web/packages/dSTEM获取）。