Two edge-count tests and relevance analysis in k high-dimensional samples

TL;DR

This paper introduces new nonparametric edge-count tests for high-dimensional k-sample relevance analysis, extending graph-based methods to handle large, unequal sample sizes with proven power advantages.

Contribution

It proposes two distribution-free edge-count test statistics for relevance analysis in high dimensions, with asymptotic null distributions and power improvements over existing methods.

Findings

Proposed tests are distribution-free and applicable to large, unequal samples.

Asymptotic null distributions are derived for the new statistics.

Simulation and real data demonstrate the effectiveness of the methods.

Abstract

For the task of relevance analysis, the conventional Tukey's test may be applied to the set of all pairwise comparisons. However, there were few studies that discuss both nonparametric k-sample comparisons and relevance analysis in high dimensions. Our aim is to capture the degree of relevance between combined samples and provide additional insights and advantages in high-dimensional k-sample comparisons. Our solution is to extend a graph-based two-sample comparison and investigate its availability for large and unequal sample sizes. We propose two distribution-free test statistics based on between-sample edge counts and measure the degree of relevance by standardized counts. The asymptotic permutation null distributions of the proposed statistics are derived, and the power gain is proved when the sample sizes are smaller than the square root of the dimension. We also discuss different edge costs in the graph to compare the parameters of the distributions. Simulation comparisons and real data analysis of tumors and images further convince the value of our proposed method. Software implementing the relevance analysis is available in the R package Relevance.