Bent-cable quantile regression model

This article considers a bent-cable quantile regression model that comprises two linear segments but is smoothly jointed by a quadratic bend. This model is very flexible to allow the relationship between the response variable and a covariate of interest to change gradually or abruptly across a change point value in the covariate. However, due to the non-differentiability of the objective function in quantile regression, it is challenge to estimate the unknown parameters. Our work aims to develop a gradient-search algorithm to obtain the estimators of the regression coefficients and the change point location. We establish the asymptotic properties of proposed estimators by using the modern empirical processes theory. Monte Carlo simulation studies and an economic empirical application illustrate the good performance of our procedures.