Confidence Statements for Ordering Quantiles

TL;DR

This paper introduces Quor, a nonparametric method for comparing population quantiles using order statistics, suitable for high-dimensional data, with exact computations and demonstrated effectiveness on biomedical datasets.

Contribution

The paper presents Quor, a novel nonparametric approach for quantile comparison that is computationally efficient and applicable to high-dimensional data without relying on asymptotic approximations.

Findings

Quor performs well in high-dimensional biomedical data classification.

Exact distribution calculations enable accurate quantile comparisons.

Quor is computationally feasible with quadratic-time dynamic programming.

Abstract

This work proposes Quor, a simple yet effective nonparametric method to compare independent samples with respect to corresponding quantiles of their populations. The method is solely based on the order statistics of the samples, and independence is its only requirement. All computations are performed using exact distributions with no need for any asymptotic considerations, and yet can be run using a fast quadratic-time dynamic programming idea. Computational performance is essential in high-dimensional domains, such as gene expression data. We describe the approach and discuss on the most important assumptions, building a parallel with assumptions and properties of widely used techniques for the same problem. Experiments using real data from biomedical studies are performed to empirically compare Quor and other methods in a classification task over a selection of high-dimensional data sets.