Multiple Testing of Local Extrema for Detection of Structural Breaks in Piecewise Linear Models

In this paper, we propose a new generic method for detecting the number and locations of change points in piecewise linear models.Our method transforms the change point detection problem into identifying local extrema through kernel smoothing and differentiation of the data sequence.By computing p-values for all local extrema based on the derived peak height distributions of the derivatives of smooth Gaussian processes, we utilize the Benjamini-Hochberg procedure to identify significant local extrema as the detected change points.Our method effectively distinguishes between two types of change points: continuous breaks (Type I) and jumps (Type II).We study three scenarios of piecewise linear signals: pure Type I, pure Type II and a mixture of both.The results demonstrate that our proposed method ensures asymptotic control of the False Discovery Rate (FDR) and power consistency as the sequence length, slope changes, and jump size increase.Furthermore, compared to traditional change point detection methods based on recursive segmentation, our approach requires only one instance of multiple-testing across all candidate local extrema, thereby achieving the smallest computational complexity proportional to the data sequence length.Additionally, numerical studies illustrate that our method maintains FDR control and power consistency, even in non-asymptotic situations with moderate