Quantile estimation and comparing two independent groups with an approach based on percentile bootstrap

Although the most common approach for comparing two independent groups is on the basis of some measure of location, determination of the differences in the tails of the groups is often of interest. In this study, Harrell–Davis estimator, Sfakianakis–Verginis estimators and default quantile estimator of R are used in conjunction with a percentile bootstrap method with the aim of comparing two independent groups via the quantiles, and the relative efficiencies of Harrell–Davis and Sfakianakis–Verginis estimators are compared. General performance of Sfakianakis–Verginis estimators was much better than Harrell–Davis estimator in terms of both saving actual type I error and relative efficiency.