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<p>This study revisits Hotelling’s <i>T</i><sup>2</sup> (HT) tests for one- and two-sample mean problems, introduces a family of scaled Hotelling’s <i>T</i><sup>2</sup>-type tests and develops two omnibus tests, termed Omnibus Hotelling’s <i>T</i><sup>2</sup> (HT-O), for both cases. Furthermore, the authors analyze the powers of the HT-O tests through the asymptotic null distributions of the scaled Hotelling’s <i>T</i><sup>2</sup>-type tests. Extensive simulation results demonstrate that the proposed HT-O tests effectively control Type I error and maintain high power under complex correlation structures, outperforming the classical HT tests in various scenarios. Applications to anti-depressant imipramine efficacy and α-amylase activity further highlight the superior performance and practical utility of the HT-O tests.</p>

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The Hotelling’s T2 Tests Revisited

  • 期刊论文

  • 发表日期：

    2025年12月13日

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  • Jing Zhou,
  • Yan Chen,
  • Jingxin Yan,
  • Sha Fang

摘要

This study revisits Hotelling’s T2 (HT) tests for one- and two-sample mean problems, introduces a family of scaled Hotelling’s T2-type tests and develops two omnibus tests, termed Omnibus Hotelling’s T2 (HT-O), for both cases. Furthermore, the authors analyze the powers of the HT-O tests through the asymptotic null distributions of the scaled Hotelling’s T2-type tests. Extensive simulation results demonstrate that the proposed HT-O tests effectively control Type I error and maintain high power under complex correlation structures, outperforming the classical HT tests in various scenarios. Applications to anti-depressant imipramine efficacy and α-amylase activity further highlight the superior performance and practical utility of the HT-O tests.