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An overview of tests on high-dimensional means

Author

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  • Huang, Yuan
  • Li, Changcheng
  • Li, Runze
  • Yang, Songshan

Abstract

Testing high-dimensional means has many applications in scientific research. For instance, it is of great interest to test whether there is a difference of gene expressions between control and treatment groups in genetic studies. This can be formulated as a two-sample mean testing problem. However, the Hotelling T2 test statistic for the two-sample mean problem is no longer well defined due to singularity of the sample covariance matrix when the sample size is less than the dimension of data. Over the last two decades, the high-dimensional mean testing problem has received considerable attentions in the literature. This paper provides a selective overview of existing testing procedures in the literature. We focus on the motivation of the testing procedures, the insights into how to construct the test statistics and the connections, and comparisons of different methods.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:jmvana:v:188:y:2022:i:c:s0047259x21000919
    DOI: 10.1016/j.jmva.2021.104813
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    References listed on IDEAS

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    Cited by:

    1. Reza Modarres, 2024. "Hotelling $$T^2$$ T 2 test in high dimensions with application to Wilks outlier method," Statistical Papers, Springer, vol. 65(8), pages 5203-5218, October.
    2. Li, Jun, 2023. "Finite sample t-tests for high-dimensional means," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    3. David M. Ritzwoller & Joseph P. Romano & Azeem M. Shaikh, 2024. "Randomization Inference: Theory and Applications," Papers 2406.09521, arXiv.org.

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