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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年8月22日

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  • Ruizhe Jiang,
  • Xiaowen Huang,
  • Yunlu Jiang

摘要

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.