Small-sample solution to the two-sample problem for quantiles using melded random confidence intervals

Abstract

A new nonparametric solution to the two-sample problem for quantiles is proposed. This solution is applicable to small samples and/or extreme quantiles, and it prioritizes limiting Type I error to the indicated level of significance over optimizing power or confidence interval width. Aside from continuity, no assumptions about the distributions are made. In this approach, nonparametric random confidence intervals obtained from the samples are “melded,” resulting in a nonparametric confidence interval for the difference between the two population quantiles with a specified confidence level. Simulations and an application to lumber strength characteristics are exhibited.

Citation

Arvanitis, Matthew A. 2022. Small-sample solution to the two-sample problem for quantiles using melded random confidence intervals. Research Paper FPL-RP-713. Madison, WI: U.S. Department of Agriculture, Forest Service, Forest Products Laboratory. 15 p.