Broken-stick quantile regression model with multiple change points

The broken-stick quantile regression model with multiple change points can characterize a non linear relationship between a response variable and a threshold covariate to change across some values in the domain. However, the estimation and statistical inference of regression coefficients and change points are challenging, due to the non smoothness of the loss function when the locations of the change points are unknown. This article aims to propose a computationally efficient method to estimate the change points and regression coefficients simultaneously via a bent-cable smoothing function that smoothes each change point location in a shrinking neighborhood for prior known the number of change points. The asymptotic properties of the proposed estimators are established. Further, we propose a computationally efficient technique to determine the number of change points for the broken-stick quantile regression model. Monte Carlo simulation results show that the proposed approaches work well in finite samples. Two applications of the maximal running speed data and the global temperature data are used to illustrate the proposed approach.