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<p>In this paper, we investigate the high-dimensional mean vector testing problem with fewer observations than the dimension. We revisit a kind of test which belongs to the supremum-type statistic and propose a novel test by the combination of the maximum and minimum values among all component tests. The asymptotic null distributions of two tests are obtained and the asymptotical powers against sparse alternatives are also investigated under weak conditions. Simulation results show that these two tests can control empirical sizes well. Our novel test can gain desirable powers. A real data example about Electro-Encephalo Gram measurements also demonstrates that our proposed test has desirable numerical performances.</p>

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Testing High-Dimensional Means for Sparse Signals

  • 期刊论文

  • 发表日期：

    2025年5月5日

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  • Jiayan Zhu,
  • Xiaochen Yu,
  • Dongdong Pan,
  • Zhengbang Li

摘要

In this paper, we investigate the high-dimensional mean vector testing problem with fewer observations than the dimension. We revisit a kind of test which belongs to the supremum-type statistic and propose a novel test by the combination of the maximum and minimum values among all component tests. The asymptotic null distributions of two tests are obtained and the asymptotical powers against sparse alternatives are also investigated under weak conditions. Simulation results show that these two tests can control empirical sizes well. Our novel test can gain desirable powers. A real data example about Electro-Encephalo Gram measurements also demonstrates that our proposed test has desirable numerical performances.