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An adaptive two-sample test for high-dimensional means

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  • Gongjun Xu
  • Lifeng Lin
  • Peng Wei
  • Wei Pan

Abstract

Several two-sample tests for high-dimensional data have been proposed recently, but they are powerful only against certain alternative hypotheses. In practice, since the true alternative hypothesis is unknown, it is unclear how to choose a powerful test. We propose an adaptive test that maintains high power across a wide range of situations and study its asymptotic properties. Its finite-sample performance is compared with that of existing tests. We apply it and other tests to detect possible associations between bipolar disease and a large number of single nucleotide polymorphisms on each chromosome based on data from a genome-wide association study. Numerical studies demonstrate the superior performance and high power of the proposed test across a wide spectrum of applications.

Suggested Citation

  • Gongjun Xu & Lifeng Lin & Peng Wei & Wei Pan, 2016. "An adaptive two-sample test for high-dimensional means," Biometrika, Biometrika Trust, vol. 103(3), pages 609-624.
    • Handle: RePEc:oup:biomet:v:103:y:2016:i:3:p:609-624.
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    File URL: http://hdl.handle.net/10.1093/biomet/asw029
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    References listed on IDEAS

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    1. Chen, Song Xi & Li, Jun & Zhong, Pingshou, 2014. "Two-Sample Tests for High Dimensional Means with Thresholding and Data Transformation," MPRA Paper 59815, University Library of Munich, Germany.
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    Cited by:

    1. Li, Jun, 2023. "Finite sample t-tests for high-dimensional means," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    2. He, Daojiang & Liu, Huanyu & Xu, Kai & Cao, Mingxiang, 2021. "Generalized Schott type tests for complete independence in high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    3. Anders Bredahl Kock & David Preinerstorfer, 2024. "Enhanced power enhancements for testing many moment equalities: Beyond the $2$- and $\infty$-norm," Papers 2407.17888, arXiv.org, revised Oct 2024.
    4. He, Yong & Zhang, Mingjuan & Zhang, Xinsheng & Zhou, Wang, 2020. "High-dimensional two-sample mean vectors test and support recovery with factor adjustment," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).
    5. Yu, Xiufan & Yao, Jiawei & Xue, Lingzhou, 2024. "Power enhancement for testing multi-factor asset pricing models via Fisher’s method," Journal of Econometrics, Elsevier, vol. 239(2).
    6. Huang, Yuan & Li, Changcheng & Li, Runze & Yang, Songshan, 2022. "An overview of tests on high-dimensional means," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    7. Zhang, Huaiyu & Wang, Haiyan, 2021. "A more powerful test of equality of high-dimensional two-sample means," Computational Statistics & Data Analysis, Elsevier, vol. 164(C).
    8. Chen, Song Xi & Guo, Bin & Qiu, Yumou, 2023. "Testing and signal identification for two-sample high-dimensional covariances via multi-level thresholding," Journal of Econometrics, Elsevier, vol. 235(2), pages 1337-1354.
    9. Ghosh, Santu & Ayyala, Deepak Nag & Hellebuyck, Rafael, 2021. "Two-sample high dimensional mean test based on prepivots," Computational Statistics & Data Analysis, Elsevier, vol. 163(C).
    10. Long Feng & Tiefeng Jiang & Binghui Liu & Wei Xiong, 2020. "Max-sum tests for cross-sectional dependence of high-demensional panel data," Papers 2007.03911, arXiv.org.

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