Estimation in a change-point nonlinear quantile model

This paper considers nonlinear quantile model, first without and then with change-points. This estimation method, which as a particular case includes median model, is more robust with respect to other traditional methods when model errors contain outliers. Under relatively weak assumptions, the convergence rate of quantile estimator of parameters in a nonlinear model is proved. If the model contains multiple change-points, the convergence rate and asymptotic distribution of change-point and of regression parameter estimators are obtained. Numerical study by Monte Carlo simulations shows the performance of the proposed method for nonlinear model with change-points.