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A two-sample test for high-dimensional mean vectors via double verification

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  • Ruizhe Jiang

    (Jinan University)

  • Xiaowen Huang

    (Jinan University)

  • Yunlu Jiang

    (Jinan University)

Abstract

Testing the equality of two high-dimensional mean vectors is a fundamental and important statistical problem. The majority of existing methodological frameworks are limited to either dense or sparse cases. In this paper, we propose a novel framework that incorporates a double validation test statistic designed to be valid for both dense and sparse alternatives by combining the test statistic via the random integration of the difference technique and the extreme-type test statistic. The new framework enables a more tailored and efficient process, contingent on the specific circumstances. Additionally, we propose a data-driven procedure for selecting weight to increase the power of the proposed test. Furthermore, we show the asymptotic properties of the proposed test. Numerical simulations and a real data analysis illustrate the promising performances of our proposed approach.

Suggested Citation

  • Ruizhe Jiang & Xiaowen Huang & Yunlu Jiang, 2025. "A two-sample test for high-dimensional mean vectors via double verification," Statistical Papers, Springer, vol. 66(6), pages 1-24, October.
    • Handle: RePEc:spr:stpapr:v:66:y:2025:i:6:d:10.1007_s00362-025-01744-4
    DOI: 10.1007/s00362-025-01744-4
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    References listed on IDEAS

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