We investigate one/two-sample mean tests for high-dimensional compositional data when the number of variables is comparable with the sample size, as commonly encountered in microbiome research. Existing methods mainly focus on max-type test statistics which are suitable for detecting sparse signals. However, in this paper, we introduce a novel approach using sum-type test statistics which are capable of detecting weak but dense signals. By establishing the asymptotic independence between the max-type and sum-type test statistics, we further propose a combined max-sum type test to cover both cases. We derived the asymptotic null distributions and power functions for these test statistics. Simulation studies demonstrate the superiority of our max-sum type test statistics which exhibit robust performance regardless of data sparsity.

翻译：本文研究了当变量个数与样本量相当的高维成分数据（常见于微生物组研究）的单样本/双样本均值检验问题。现有方法主要关注适用于检测稀疏信号的极大值型检验统计量。然而，本文提出了一种采用和型检验统计量的新方法，该方法能够检测微弱但密集的信号。通过建立极大值型与和型检验统计量的渐近独立性，我们进一步提出了一种综合极大-求和型检验方法以覆盖两种情况。我们推导了这些检验统计量的渐近零分布和势函数。模拟研究表明，我们的极大-求和型检验统计量无论数据稀疏性如何均表现出稳健性能，具有显著优越性。