We provide novel, high-order accurate methods for nonparametric inference on quantile differences between two populations in both unconditional and conditional settings. These quantile differences identify (conditional) quantile treatment effects under (conditional) independence of a binary treatment and potential outcomes. Our methods use the probability integral transform and a Dirichlet (rather than Gaussian) reference distribution to pick appropriate L-statistics as confidence interval endpoints, achieving high-order accuracy.
fractional order statistics
We propose a nonparametric method to construct confidence intervals for quantile marginal effects (i.e., derivatives of the conditional quantile function). Under certain conditions, a quantile marginal effect equals a causal (structural) effect in a general nonseparable model, or equals an average thereof within a particular subpopulation. The high-order accuracy of our method is derived. Simulations and an empirical example demonstrate the new method's favorable performance and practical use. Code for the new method is provided
Using and extending fractional order statistic theory, we characterize the O(n−1) coverage probability error of the previously proposed confidence intervals for population quantiles using L-statistics as endpoints in Hutson (1999). We derive an analytic expression for the n−1 term, which may be used to calibrate the nominal coverage level to get O(n−3/2log(n)) coverage error. Asymptotic power is shown to be optimal. Using kernel smoothing, we propose a related method for nonparametric inference on conditional quantiles.
This has now been replaced by working paper WP 16-20