Quantile LASSO Change Point Estimation Of Two Kinds Of Linear Models

The problem of change points has been a heated issue in statistics since the 1970 s.Linear regression model and linear panel data model are widely used in economics and finance.Application of quantile LASSO method to two models can be used as an important method for change point estimation.On the basis of the existing study,this paper studies the change point estimation problems of linear regression model and linear panel data model.The details are as following:First,The change point estimation of linear regression model is studied,and the quantile LASSO estimator is given.We discussed the consistency of the estimated position of the change points when the estimated number of change points is equal to the true number of change points.It is proved that when the estimated number of change points is more than the real number,the Hausdorff distance of the estimated change point set and the real change point set is within a certain range.Simulations demonstrate the estimated performance of quantile LASSO with two tuning parameters.Secondly,the change point estimation problem of linear panel data is studied,We modify the quantile LASSO method to apply to the linear panel data structure.Prove the consistency of model estimated parameters and real parameters under given conditions,and the probability that the estimated number of change points is less than the true number approaches zero.Simulation confirms the robustness of quantile LASSO with two distributions.Finally,we summarized the main work of this paper and put forward the contents that need further investigation.