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<p>The problem of comparing mean vectors in high-dimensional two-sample scenarios has been extensively researched. In this paper, we assume that the precision matrix of data follows a linear structure and introduce a maximum-type test statistic for sparse alternative hypotheses. We demonstrate the asymptotic independence between our proposed maximum-type test statistic and an existing sum-type test statistic. Based on this, we propose a Cauchy combination test procedure that performs effectively in both dense and sparse alternative scenarios. Simulation studies confirm that our proposed tests outperform other adaptive tests, particularly in cases with strong correlation structures.</p>

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An adaptive approach for testing high-dimensional location parameters with structured correlations

  • 期刊论文

  • 发表日期：

    2025年1月27日

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  • Liu Yanhong,
  • Zhao Ping,
  • Feng Long,
  • Wang Zhaojun

摘要

The problem of comparing mean vectors in high-dimensional two-sample scenarios has been extensively researched. In this paper, we assume that the precision matrix of data follows a linear structure and introduce a maximum-type test statistic for sparse alternative hypotheses. We demonstrate the asymptotic independence between our proposed maximum-type test statistic and an existing sum-type test statistic. Based on this, we propose a Cauchy combination test procedure that performs effectively in both dense and sparse alternative scenarios. Simulation studies confirm that our proposed tests outperform other adaptive tests, particularly in cases with strong correlation structures.