A Comparison Of Nonparametric Conditional Quantile Estimation

In the 1970s,Koenker and Bassett proposed the quantile regression(QR),which can make up for the deficiencies of the mean regression and more fully describe the conditional distribution information of the dependent variables,especially in tail regions.But,in application,the relationship between variables may be nonlinear and more complicated.In this case,nonparametric quantile regression models is proposed.In this paper,based on the nonparametric quantile regression model,the nonparametric conditional quantile regression estimation based on the check function,the nonparametric conditional cumulative distribution function and the conditional quantile estimation,and the nonparametric condition based on the quantile function are theoretically compared.Theoretical research shows that under the the non-parametric location scale model,if the assumption conditions are satisfied,the non-parametric conditional quantile regression estimation method based on the quantile function has the best estimation effect when the data has unbounded support.Meanwhile,we compare the estimated accuracy about these methods by Monte Carlo simulations,which is consistent with the theoretical comparison.Finally,we take the typical wage data in the Mid-Atlantic region as an example of non-parametric quantile regression model to study the impact of age on wages at different quantile levels.From empirical angle,we compare the estimators of conditional quantile functions that are based on the check function and the quantile function,we find that the conditional quantile estimators based on the quantile function can obtain more reasonable conditional quantiles and its first derivative estimates.