Multiple Change-Points Estimation in Linear Regression Models via an Adaptive LASSO Expectile Loss Function

In this paper, a linear model with possible change-points is considered. The errors do not satisfy the classical homoscedasticity assumption considered in standard linear regression settings. Both the change-points and the coefficients are estimated through an expectile loss function. An adaptive LASSO penalty is added to simultaneously perform feature selection. The convergence rates of the obtained estimators are given, and we show that the coefficients’ estimators fulfill the sparsity property in each phase of the model. We also give a criterion for selecting the number of change-points. A numerical study is performed to compare the performance of the proposed penalized expectile method with the ordinary least squares and the quantile methods also penalized. Finally, a real data application on weather data is provided to validate the analytical results.