Title:  Multiple Testing of Local Extrema for Detection of Change Points

Abstract: We propose a new approach to detect the number and location of change points in piecewise linear models under stationary Gaussian noise. Our method transforms the change point detection problem into identifying significant 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 derivatives of smooth Gaussian processes, we utilize the Benjamini-Hochberg procedure to identify significant local extrema as the detected change points. The algorithm provides asymptotic strong control of the False Discovery Rate (FDR) and power consistency, as the length of the sequence and the size of jumps get large. Simulations show that FDR levels are maintained in non-asymptotic conditions and guide the choice of smoothing bandwidth. 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 proportionate to the data sequence length.