2014): "A Direct Approach to Inference in Nonparametric and Semiparametric Quantile Models," Working paper

This paper makes two main contributions to inference for conditional quantiles. First, we construct a generic con\u85dence interval for a conditional quantile from any given estimator of the conditional quantile via the direct approach. Our generic con\u85dence interval makes use of two estimates of the conditional quantile function evaluated at two appropriately chosen quantile levels. In contrast to the standard Wald type con\u85dence interval, ours circumvents the need to estimate the conditional density function of the dependent variable given the covariate. We show that our new con\u85dence interval is asymptotically valid for any quantile function (parametric, nonparametric, or semiparametric), any conditional quantile estimator (standard kernel, local polynomial or sieve estimates), and any data structure (random samples, time series, or censored data), provided that certain weak convergence of the conditional quantile process holds for the preliminary quantile estimator. In the same spirit, we also construct a generic con dence band for the conditional quantile function across a range of covariate values. Second, we use a speci\u85c estimator, the Yang-Stute (also known as the symmetrized k-NN) estimator for a nonparametric quantile function, and two popular semiparametric quantile functions t