On testing mean of high dimensional compositional data

Qianqian Jiang; Wenbo Li; Zeng Li

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arXiv · 2404.08355

On testing mean of high dimensional compositional data

Qianqian Jiang·Wenbo Li·Zeng Li

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Abstract

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.

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Qianqian Jiang, Wenbo Li, Zeng Li. 2024-04-12. On testing mean of high dimensional compositional data. https://arxiv.org/abs/2404.08355

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