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Two-sample test of stochastic block models

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  • Wu, Qianyong
  • Hu, Jiang

Abstract

In this paper, we consider the problem of two-sample test of large networks with community structures. A test statistic is proposed based on the maximum entry of the difference between the two adjacency matrices. Asymptotic null distribution is derived, and the asymptotic power guarantee against the alternative hypothesis is provided. The simulations and real data examples show that the proposed test statistic performs well.

Suggested Citation

  • Wu, Qianyong & Hu, Jiang, 2024. "Two-sample test of stochastic block models," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:csdana:v:192:y:2024:i:c:s0167947323002141
    DOI: 10.1016/j.csda.2023.107903
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    References listed on IDEAS

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    1. Peter J. Bickel & Purnamrita Sarkar, 2016. "Hypothesis testing for automated community detection in networks," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 253-273, January.
    2. Jianwei Hu & Hong Qin & Ting Yan & Yunpeng Zhao, 2020. "Corrected Bayesian Information Criterion for Stochastic Block Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(532), pages 1771-1783, December.
    3. Kehui Chen & Jing Lei, 2018. "Network Cross-Validation for Determining the Number of Communities in Network Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 241-251, January.
    4. Jianwei Hu & Jingfei Zhang & Hong Qin & Ting Yan & Ji Zhu, 2021. "Using Maximum Entry-Wise Deviation to Test the Goodness of Fit for Stochastic Block Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(535), pages 1373-1382, July.
    5. Tianxi Li & Elizaveta Levina & Ji Zhu, 2020. "Network cross-validation by edge sampling," Biometrika, Biometrika Trust, vol. 107(2), pages 257-276.
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