Simultaneous change-point detection and curve estimation

In this work, we focus on a nonparametric regression model that accounts for discontinuities. We propose a method called Simultaneous CHange-point detection And Curve Estimation (SCHACE) for effectively detecting jumps in a data sequence and accurately capturing nonlinear trends between these jumps in the mean curve. The SCHACE is a unified regularization framework that incorporates two statistical tools: the normalized fused Lasso for change-point detection and B-splines for curve estimation. Notably, this approach is a single-step method that does not require iteration and is straightforward to implement. We demonstrate the advantages of the SCHACE by simulated and real-world data examples.