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：本文提出了一种在平稳高斯噪声下检测分段线性模型中结构突变或变点数量与位置的新通用方法。该方法通过核平滑与数据序列微分，将变点检测问题转化为局部极值（局部极大值与局部极小值）的识别问题。基于平滑高斯过程的峰值高度分布为所有局部极值计算p值后，我们采用Benjamini-Hochberg程序筛选显著的局部极值作为检测到的变点。本方法能区分两类变点：连续型突变（I型）与跳跃型突变（II型）。我们研究了分段线性信号的三种情形：纯I型、纯II型以及I型与II型混合的变点。结果表明，随着序列长度、斜率变化量与跳跃幅度的增加，所提方法能保证错误发现率（FDR）的渐近控制与检验功效的一致性。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。数值研究进一步表明，即使在斜率变化或跳跃幅度不大的非渐近情况下，本方法仍能保持FDR控制与功效一致性。我们已将方法实现于R软件包"dSTEM"中（可通过https://cran.r-project.org/web/packages/dSTEM获取）。