A direct approach to inference in nonparametric and semiparametric quantile models

We construct a generic confidence interval for a conditional quantile via the direct approach. It avoids estimating the conditional density function of the dependent variable given the covariate and is asymptotically valid for any conditional quantile, any conditional quantile estimator, and any data structure, provided that certain weak convergence of the conditional quantile process holds for the original quantile estimator. We also construct a generic confidence band for the conditional quantile function across a range of covariate values. By using Yang-Stute estimator and two semiparametric quantile functions, we demonstrate the flexibility and simplicity of the direct approach. The advantages of our new confidence intervals are borne out in a simulation study.