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AUGUST: An Interpretable, Resolution-based Two-sample Test
Volume 2, Issue 3 (2024), pp. 357–367
Benjamin Brown   Kai Zhang  

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https://doi.org/10.51387/23-NEJSDS54
Pub. online: 15 December 2023      Type: Methodology Article      Open accessOpen Access
Area: Statistical Methodology

Accepted
4 September 2023
Published
15 December 2023

Abstract

Two-sample testing is a fundamental problem in statistics. While many powerful nonparametric methods exist for both the univariate and multivariate context, it is comparatively less common to see a framework for determining which data features lead to rejection of the null. In this paper, we propose a new nonparametric two-sample test named AUGUST, which incorporates a framework for interpretation while maintaining power comparable to existing methods. AUGUST tests for inequality in distribution up to a predetermined resolution using symmetry statistics from binary expansion. Designed for univariate and low to moderate-dimensional multivariate data, this construction allows us to understand distributional differences as a combination of fundamental orthogonal signals. Asymptotic theory for the test statistic facilitates p-value computation and power analysis, and an efficient algorithm enables computation on large data sets. In empirical studies, we show that our test has power comparable to that of popular existing methods, as well as greater power in some circumstances. We illustrate the interpretability of our method using NBA shooting data.

Supplementary material

 Supplementary Material
Supplementary material for AUGUST.

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© 2024 New England Statistical Society
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Open access article under the CC BY license.

Keywords
Distributional difference Interpretability Power Symmetry Visualization

Funding
This research is partially supported by NSF grants DMS-1613112, IIS-1633212, DMS-1916237, and DMS-2152289.

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