A new graph-based two-sample test for multivariate and object data

TL;DR

This paper introduces a novel graph-based two-sample test applicable to multivariate and non-Euclidean data, demonstrating improved power and broad applicability through simulations and real-world examples.

Contribution

It proposes a new similarity graph-based test that effectively detects both location and scale differences in diverse data types, addressing limitations of existing methods.

Findings

Exhibits substantial power gains in simulations

Works well with large datasets due to asymptotic null distribution

Successfully applied to covariate balance and network data comparison

Abstract

Two-sample tests for multivariate data and especially for non-Euclidean data are not well explored. This paper presents a novel test statistic based on a similarity graph constructed on the pooled observations from the two samples. It can be applied to multivariate data and non-Euclidean data as long as a dissimilarity measure on the sample space can be defined, which can usually be provided by domain experts. Existing tests based on a similarity graph lack power either for location or for scale alternatives. The new test utilizes a common pattern that was overlooked previously, and works for both types of alternatives. The test exhibits substantial power gains in simulation studies. Its asymptotic permutation null distribution is derived and shown to work well under finite samples, facilitating its application to large data sets. The new test is illustrated on two applications: The assessment of covariate balance in a matched observational study, and the comparison of network data under different conditions.