Nonparametric inference on conditional quantile differences and linear combinations, using L-statistics

We provide novel methods for nonparametric inference on quantile differences between two populations in both unconditional and conditional settings. Under (conditional) independence of a binary treatment and potential outcomes, these quantile differences are (conditional) quantile treatment effects. These methods achieve highorder accuracy by using the probability integral transform and a Dirichlet (rather than Gaussian) reference distribution to pick appropriate L-statistics as confidence interval endpoints. We propose related methods for joint inference on multiple quantiles and inference on linear combinations of quantiles, again in both unconditional and conditional settings. For the case of smoothing over continuous covariates, optimal bandwidth and coverage probability rates are derived for all methods. Simulations using a plug-in bandwidth show the new method’s equal-tailed confidence intervals to have a favorable combination of robust coverage accuracy and short length compared with existing approaches. Code for methods, simulations, and empirical examples is provided. JEL: C21