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A New Graph-Based Two-Sample Test for Multivariate and Object Data

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  • Hao Chen
  • Jerome H. Friedman

Abstract

Two-sample tests for multivariate data and especially for non-Euclidean data are not well explored. This article 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 uses 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 datasets. 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.

Suggested Citation

  • Hao Chen & Jerome H. Friedman, 2017. "A New Graph-Based Two-Sample Test for Multivariate and Object Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 397-409, January.
    • Handle: RePEc:taf:jnlasa:v:112:y:2017:i:517:p:397-409
    DOI: 10.1080/01621459.2016.1147356
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    Cited by:

    1. Zhang, Jin-Ting & Guo, Jia & Zhou, Bu, 2024. "Testing equality of several distributions in separable metric spaces: A maximum mean discrepancy based approach," Journal of Econometrics, Elsevier, vol. 239(2).
    2. Lovato, Ilenia & Pini, Alessia & Stamm, Aymeric & Vantini, Simone, 2020. "Model-free two-sample test for network-valued data," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    3. Pini, Alessia & Stamm, Aymeric & Vantini, Simone, 2018. "Hotelling’s T2 in separable Hilbert spaces," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 284-305.
    4. Zhi Peng Ong & Aixiang Andy Chen & Tianming Zhu & Jin-Ting Zhang, 2023. "Testing Equality of Several Distributions at High Dimensions: A Maximum-Mean-Discrepancy-Based Approach," Mathematics, MDPI, vol. 11(20), pages 1-21, October.
    5. Jun Li, 2018. "Asymptotic normality of interpoint distances for high-dimensional data with applications to the two-sample problem," Biometrika, Biometrika Trust, vol. 105(3), pages 529-546.
    6. Qiu, Tao & Zhang, Qintong & Fang, Yuanyuan & Xu, Wangli, 2024. "Testing homogeneity in high dimensional data through random projections," Journal of Multivariate Analysis, Elsevier, vol. 200(C).

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