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<p>In this paper, the hypothesis testing for a linear combination of mean vectors of several populations is considered in a high-dimensional context while taking homoskedasticity into account. We suggest a ridgelized Hotelling’s <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(T^{2}\)</EquationSource> </InlineEquation> (RHT) test statistic and derive its asymptotic distribution by employing techniques from Random Matrix Theory (RMT). Since only the first fourth-order moments matching with the normal distribution are required, this allows the RHT test to handle arbitrary distributions of high-dimensional data. An extensive simulation investigation reveals that the RHT test performs well based on empirical sizes and powers and is more robust than other competitive tests, especially with strongly correlated data.</p>

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A ridgelized test for high-dimensional linear hyplothesis of mean vectors

  • 期刊论文

  • 发表日期：

    2025年12月10日

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  • Jianghao Li,
  • Li Yang,
  • Qiuyan Zhang,
  • Zhenzhen Niu,
  • Zhidong Bai

摘要

In this paper, the hypothesis testing for a linear combination of mean vectors of several populations is considered in a high-dimensional context while taking homoskedasticity into account. We suggest a ridgelized Hotelling’s \(T^{2}\) (RHT) test statistic and derive its asymptotic distribution by employing techniques from Random Matrix Theory (RMT). Since only the first fourth-order moments matching with the normal distribution are required, this allows the RHT test to handle arbitrary distributions of high-dimensional data. An extensive simulation investigation reveals that the RHT test performs well based on empirical sizes and powers and is more robust than other competitive tests, especially with strongly correlated data.