Convergence rate of a new non-parametric change-point estimator within a linear model

We consider data initially derived from a homoscedastic linear model that undergoes a change at an unknown point in time, such as a change in model (not necessarily linear) or heteroscedasticity. Based on an idea of the sum of the squares of the residuals penalized introduced in Bardet ( 2025), we propose a new version of this criterion for estimating the change point. In the very general nonparametric framework we have adopted, we demonstrate that the convergence rate of this estimator is the same as in the parametric case to within a logarithmic term. To do this, we use concentration inequalities for sub-exponential variables.