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Multi-sample hypothesis testing of high-dimensional mean vectors under covariance heterogeneity

Author

Listed:
  • Lixiu Wu

    (Northeast Normal University)

  • Jiang Hu

    (Northeast Normal University)

Abstract

In this paper, we focus on the hypothesis testing problem of the mean vectors of high-dimensional data in the multi-sample case. We propose two maximum-type statistics and apply a parametric bootstrap technique to compute the critical values. Unlike previous hypothesis testing methods that heavily depend on the structural assumptions of the unknown covariance matrix, the proposed methods accommodate a general covariance structure. Additionally, we introduce screening-based testing procedures to enhance the power of our tests. These test procedures do not require the use of approximate limiting distributions for the test statistics. Finally, we obtain and verify the theoretical properties through simulation studies.

Suggested Citation

  • Lixiu Wu & Jiang Hu, 2024. "Multi-sample hypothesis testing of high-dimensional mean vectors under covariance heterogeneity," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(4), pages 579-615, August.
    • Handle: RePEc:spr:aistmt:v:76:y:2024:i:4:d:10.1007_s10463-024-00896-8
    DOI: 10.1007/s10463-024-00896-8
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    References listed on IDEAS

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    6. Jinyuan Chang & Chao Zheng & Wen‐Xin Zhou & Wen Zhou, 2017. "Simulation‐based hypothesis testing of high dimensional means under covariance heterogeneity," Biometrics, The International Biometric Society, vol. 73(4), pages 1300-1310, December.
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