Multiple change‐point detection for regression curves

Abstract

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.