Two-sample tests of high-dimensional means for compositional data
针对高维成分数据提出两样本均值等价性检验方法，基于中心化对数比变换推导检验统计量的渐近零分布，模拟和微生物组实例表明其比传统方法更有效。
Compositional data are ubiquitous in many scientific endeavours. Motivated by microbiome and metagenomic research, we consider a two-sample testing problem for high-dimensional compositional data and formulate a testable hypothesis of compositional equivalence for the means of two latent log basis vectors. We propose a test through the centred log-ratio transformation of the compositions. The asymptotic null distribution of the test statistic is derived and its power against sparse alternatives is investigated. A modified test for paired samples is also considered. Simulations show that the proposed tests can be significantly more powerful than tests that are applied to the raw and log-transformed compositions. The usefulness of our tests is illustrated by applications to gut microbiome composition in obesity and Crohn's disease.