Some Results on Comparing the Quantiles of Dependent Groups

摘要

Recently, Lombard derived an extension of the Doksum-Sievers shift function to dependent groups. This article suggests using a particular numerical method for determining the critical value, reports on the ability of the method to control the probability of a Type Ⅰ error when sample sizes are small, and it provides comparisons with methods aimed at comparing deciles. It is found that for continuous distributions, Lombard's method performs well and in particular has high power relative to the other two methods considered. But when tied values can occur, now it can have relatively poor power; a method based on the Harrell-Davis estimator is found to give more satisfactory results.