In this repo, 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 centered 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.
Reference:
Cao, Y., Lin, W. and Li, H. (2018). Two-sample tests of high-dimensional means for compositional data, Biometrika.
Please see https://academic.oup.com/biomet/article/105/1/115/4591648 and http://www.math.pku.edu.cn/teachers/linw/papers/cao_lin_li18.pdf.