Variable data driven bandwidth choice in nonparametric quantile regression

The choice of a smoothing parameter or bandwidth is crucial when applying nonparametric regression estimators. In nonparametric mean regression various methods for bandwidth selection exists. But in nonparametric quantile regression bandwidth choice is still an unsolved problem. In this paper a selection procedure for local varying bandwidths based on the asymptotic mean squared error (MSE) of the local linear quantile estimator is discussed. To estimate the unknown quantities of the MSE local linear quantile regression based on cross-validation and local likelihood estimation is used.