A Nonparametric Test of Multivariate Independence Using Graphs

Yanhui Li; Yubin Tian; Jinjuan Wang

doi:10.1002/sta4.70146

A Nonparametric Test of Multivariate Independence Using Graphs

Yanhui Li
, Yubin Tian
, Jinjuan Wang^*

^*Corresponding author for this work

School of Statistics
Shenzhen MSU-BIT University
Beijing Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

Testing whether two sets of variables are correlated is a critical problem in statistical research, and numerous methods have been proposed to address it. However, many existing approaches suffer from various limitations. To overcome these challenges, we propose a graph-based nonparametric strategy that introduces both unweighted and weighted test statistics. To our knowledge, this is the first application of the minimum distance pairing (MDP) graphs in independence testing. The novel method is not susceptible to outliers and applicable in settings where raw data is unavailable due to privacy concerns. We also establish the theoretical properties of the proposed statistics focusing on distributional characteristics and statistical inferences. Extensive numerical studies demonstrate that our approach improves power while maintaining robustness. Finally, a real data analysis further validates its superior performance.

Original language	English
Article number	e70146
Journal	Stat
Volume	15
Issue number	1
DOIs	https://doi.org/10.1002/sta4.70146
Publication status	Published - Mar 2026
Externally published	Yes

Keywords

minimum distance pairing
multivariate analysis
nonparametric independence test

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10.1002/sta4.70146

Cite this

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title = "A Nonparametric Test of Multivariate Independence Using Graphs",

abstract = "Testing whether two sets of variables are correlated is a critical problem in statistical research, and numerous methods have been proposed to address it. However, many existing approaches suffer from various limitations. To overcome these challenges, we propose a graph-based nonparametric strategy that introduces both unweighted and weighted test statistics. To our knowledge, this is the first application of the minimum distance pairing (MDP) graphs in independence testing. The novel method is not susceptible to outliers and applicable in settings where raw data is unavailable due to privacy concerns. We also establish the theoretical properties of the proposed statistics focusing on distributional characteristics and statistical inferences. Extensive numerical studies demonstrate that our approach improves power while maintaining robustness. Finally, a real data analysis further validates its superior performance.",

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T1 - A Nonparametric Test of Multivariate Independence Using Graphs

AU - Li, Yanhui

AU - Tian, Yubin

AU - Wang, Jinjuan

PY - 2026/3

Y1 - 2026/3

N2 - Testing whether two sets of variables are correlated is a critical problem in statistical research, and numerous methods have been proposed to address it. However, many existing approaches suffer from various limitations. To overcome these challenges, we propose a graph-based nonparametric strategy that introduces both unweighted and weighted test statistics. To our knowledge, this is the first application of the minimum distance pairing (MDP) graphs in independence testing. The novel method is not susceptible to outliers and applicable in settings where raw data is unavailable due to privacy concerns. We also establish the theoretical properties of the proposed statistics focusing on distributional characteristics and statistical inferences. Extensive numerical studies demonstrate that our approach improves power while maintaining robustness. Finally, a real data analysis further validates its superior performance.

AB - Testing whether two sets of variables are correlated is a critical problem in statistical research, and numerous methods have been proposed to address it. However, many existing approaches suffer from various limitations. To overcome these challenges, we propose a graph-based nonparametric strategy that introduces both unweighted and weighted test statistics. To our knowledge, this is the first application of the minimum distance pairing (MDP) graphs in independence testing. The novel method is not susceptible to outliers and applicable in settings where raw data is unavailable due to privacy concerns. We also establish the theoretical properties of the proposed statistics focusing on distributional characteristics and statistical inferences. Extensive numerical studies demonstrate that our approach improves power while maintaining robustness. Finally, a real data analysis further validates its superior performance.

KW - minimum distance pairing

KW - multivariate analysis

KW - nonparametric independence test

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M3 - Article

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SN - 2049-1573

VL - 15

JO - Stat

JF - Stat

IS - 1

M1 - e70146

ER -

A Nonparametric Test of Multivariate Independence Using Graphs

Abstract

Keywords

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