Optimal smoothing in nonparametric conditional quantile derivative function estimation

Marginal effect in nonparametric quantile regression is of special interest as it quantitatively measures how one unit change in explanatory variable heterogeneously affects dependent variable ceteris paribus at distinct quantiles. In this paper, we propose a data-driven bandwidth selection procedure based on the gradient of an unknown quantile regression function. Our method delivers the bandwidth with the oracle property in the sense that it is asymptotically equivalent to the optimal bandwidth if the true gradient were known. The results of Monte Carlo simulations are reported, and the finite sample performance of our proposed method confirms our theoretical analysis. An empirical application is also provided, showing that our proposed method delivers more reasonable and reliable quantile derivative estimates than traditional cross validation method.