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Ensemble Subsampling for Imbalanced Multivariate Two-Sample Tests

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  • L. Chen
  • W. W. Dou
  • Z. Qiao

Abstract

Some existing nonparametric two-sample tests for equality of multivariate distributions perform unsatisfactorily when the two sample sizes are unbalanced. In particular, the power of these tests tends to diminish with increasingly unbalanced sample sizes. In this article, we propose a new testing procedure to solve this problem. The proposed test, based on the nearest neighbor method by Schilling, employs a novel ensemble subsampling scheme to remedy this issue. More specifically, the test statistic is a weighted average of a collection of statistics, each associated with a randomly selected subsample of the data. We derive the asymptotic distribution of the test statistic under the null hypothesis and show that the new test is consistent against all alternatives when the ratio of the sample sizes either goes to a finite limit or tends to infinity. Via simulated data examples we demonstrate that the new test has increasing power with increasing sample size ratio when the size of the smaller sample is fixed. The test is applied to a real-data example in the field of corporate finance. Supplementary materials for this article are available online.
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  • L. Chen & W. W. Dou & Z. Qiao, 2014. "Ensemble Subsampling for Imbalanced Multivariate Two-Sample Tests," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 871-871, June.
    • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:506:p:871-871
    DOI: 10.1080/01621459.2014.899497
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    Cited by:

    1. Dumas, Bernard & Gabuniya, Tymur & Marston, Richard C., 2022. "Firms’ exposures to geographic risks," Journal of International Money and Finance, Elsevier, vol. 122(C).
    2. Meng Jiang & Brooke A. Ammerman & Qingkai Zeng & Ross Jacobucci & Alex Brodersen, 2020. "Phrase-level pairwise topic modeling to uncover helpful peer responses to online suicidal crises," Palgrave Communications, Palgrave Macmillan, vol. 7(1), pages 1-13, December.
    3. Dumas, Bernard & Gabuniya, Tymur & Marston, Richard C, 2020. "Firms' Exposures to Geographic Risks," CEPR Discussion Papers 15503, C.E.P.R. Discussion Papers.
    4. Schneider, Judith C. & Schweizer, Nikolaus, 2015. "Robust measurement of (heavy-tailed) risks: Theory and implementation," Journal of Economic Dynamics and Control, Elsevier, vol. 61(C), pages 183-203.
    5. Kaveh Ahmadian Tazehmahaleh & Hamideh Godazgar & Kevin AG Smet & Peter Hanselaer, 2022. "Multi-Channel LED Luminaires: An Object-Oriented Approach for Retail Lighting Based on the SOR Framework," Sustainability, MDPI, vol. 14(10), pages 1-17, May.
    6. Dou, Winston Wei & Taylor, Lucian A. & Wang, Wei & Wang, Wenyu, 2021. "Dissecting bankruptcy frictions," Journal of Financial Economics, Elsevier, vol. 142(3), pages 975-1000.

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