Assessing a hypothesis test for the difference between two quantiles from independent populations

An empirical distribution function estimator for the difference of order statistics from two independent populations can be used for inference between quantiles from these populations. The inferential properties of the approach are evaluated in a simulation study where different sample sizes, theoretical distributions, and quantiles are studied. Small to moderate sample sizes, tail quantiles, and quantiles which do not coincide with the expectation of an order statistic are identified as problematic for appropriate Type I error control.