Nonparametric inference on conditional quantile treatment effects using L-statistics

We provide novel methods for inference on quantile treatment effects in both uncon- ditional and conditional (nonparametric) settings. These methods achieve high-order accuracy by using the probability integral transform and a Dirichlet (rather than Gaus- sian) reference distribution. We propose related methods for joint inference on multiple quantiles and inference on linear combinations of quantiles, again in both unconditional and conditional settings. Optimal bandwidth and coverage probability rates are derived for all methods, and code is provided.