Multiple change-point detection for regression curves

Nonparametric estimation of a regression curve becomes crucial when the underlying dependence structure between covariates and responses is not explicit. While existing literature has addressed single change-point estimation for regression curves, the problem of multiple change points remains unresolved. In an effort to bridge this gap, this article introduces a nonparametric estimator for multiple change points by minimizing a penalized weighted sum of squared residuals, presenting consistent results under mild conditions. Additionally, we propose a cross-validation-based procedure that possesses the advantage of being tuning-free. Our simulation results showcase the competitive performance of these new procedures when compared with state-of-the-art methods. As an illustration of their utility, we apply these procedures to a real dataset.