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On testing mean of high dimensional compositional data

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  • Jiang, Qianqian
  • Li, Wenbo
  • Li, Zeng

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 and real data applications demonstrate the superiority of our max-sum type test statistics which exhibit robust performance regardless of data sparsity.

Suggested Citation

  • Jiang, Qianqian & Li, Wenbo & Li, Zeng, 2025. "On testing mean of high dimensional compositional data," Statistics & Probability Letters, Elsevier, vol. 222(C).
    • Handle: RePEc:eee:stapro:v:222:y:2025:i:c:s0167715225000410
    DOI: 10.1016/j.spl.2025.110396
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    References listed on IDEAS

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    1. Srivastava, Muni S., 2009. "A test for the mean vector with fewer observations than the dimension under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 518-532, March.
    2. Chen, Song Xi & Qin, Yingli, 2010. "A Two Sample Test for High Dimensional Data with Applications to Gene-set Testing," MPRA Paper 59642, University Library of Munich, Germany.
    3. Srivastava, Muni S. & Du, Meng, 2008. "A test for the mean vector with fewer observations than the dimension," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 386-402, March.
    4. Yuanpei Cao & Wei Lin & Hongzhe Li, 2018. "Two-sample tests of high-dimensional means for compositional data," Biometrika, Biometrika Trust, vol. 105(1), pages 115-132.
    5. Wei Lin & Pixu Shi & Rui Feng & Hongzhe Li, 2014. "Variable selection in regression with compositional covariates," Biometrika, Biometrika Trust, vol. 101(4), pages 785-797.
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