Abstract

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 seg-

mentation, 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

slope changes or jumps. We have implemented our method in the R package “dSTEM”.

Key words and phrases: structural breaks, change points, piecewise linear models, kernel smoothing, multiple testing, Gaussian processes, peak height distribution, and FDR

Information

Preprint No.SS-2025-0113
Manuscript IDSS-2025-0113
Complete AuthorsZhibing He, Dan Cheng, Yunpeng Zhao
Corresponding AuthorsDan Cheng
Emailschengdan@asu.edu

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Acknowledgments

The authors thank Prof. Domenico Marinucci for motivating this research problem and Prof. Armin Schwartzman for helpful discussions and valuable sugges-

tions.

Supplementary Materials

The online Supplementary Material contains the theoretical proofs, technical

derivations, and additional numerical results that support the findings of this paper. Specifically, it provides the rigorous mathematical proofs for the main the-

orems and technical lemmas, including the asymptotic distributions of the test

statistics and the error rate controls. It also outlines the detailed implementation

of the proposed multiple testing procedure for structural break detection, alongside extended simulation studies that evaluate the finite-sample performance,

power, and robustness of the methodology under various noise structures and

signal intensities.

Supplementary materials are available for download.