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A one-way MANOVA test for high-dimensional data using clustering subspaces

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  • Lu, Minyuan
  • Zhou, Bu

Abstract

This study focuses on the high-dimensional one-way analysis of variance problem, specifically, testing whether multiple population mean vectors are equal in the context of high-dimensional data. To solve the problem that classical multivariate analysis of variance (MANOVA) test statistics are undefined when the dimensionality surpasses the sample size, we propose a random permutation test using low-dimensional subspaces obtained by clustering of variables. The test statistics are derived from a one-way MANOVA decomposition for clustered variables and this approach utilizes the correlation information among variables to ensure high testing power. Simulation studies indicate that the proposed test performs well with high-dimensional data.

Suggested Citation

  • Lu, Minyuan & Zhou, Bu, 2025. "A one-way MANOVA test for high-dimensional data using clustering subspaces," Statistics & Probability Letters, Elsevier, vol. 217(C).
    • Handle: RePEc:eee:stapro:v:217:y:2025:i:c:s0167715224002621
    DOI: 10.1016/j.spl.2024.110293
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    References listed on IDEAS

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    1. Zhang, Jin-Ting & Guo, Jia & Zhou, Bu, 2017. "Linear hypothesis testing in high-dimensional one-way MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 200-216.
    2. Shen, Yanfeng & Lin, Zhengyan & Zhu, Jun, 2011. "Shrinkage-based regularization tests for high-dimensional data with application to gene set analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2221-2233, July.
    3. Schott, James R., 2007. "Some high-dimensional tests for a one-way MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1825-1839, October.
    4. Srivastava, Muni S. & Fujikoshi, Yasunori, 2006. "Multivariate analysis of variance with fewer observations than the dimension," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 1927-1940, October.
    5. Shen, Yanfeng & Lin, Zhengyan, 2015. "An adaptive test for the mean vector in large-p-small-n problems," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 25-38.
    6. Zhang, Jie & Pan, Meng, 2016. "A high-dimension two-sample test for the mean using cluster subspaces," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 87-97.
    7. Srivastava, Muni S. & Kubokawa, Tatsuya, 2013. "Tests for multivariate analysis of variance in high dimension under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 204-216.
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