On testing mean of high dimensional compositional data
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.
Cite
@article{arxiv.2404.08355,
title = {On testing mean of high dimensional compositional data},
author = {Qianqian Jiang and Wenbo Li and Zeng Li},
journal= {arXiv preprint arXiv:2404.08355},
year = {2024}
}