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Bayesian hypothesis testing for equality of high-dimensional means using cluster subspaces

Author

Listed:
  • Fang Chen

    (Center for Biologics Evaluation and Research (CBER), Food and Drug Administration)

  • Qiuchen Hai

    (Texas A&M University-San Antonio)

  • Min Wang

    (The University of Texas at San Antonio)

Abstract

The classical Hotelling’s $$T^2$$ T 2 test and Bayesian hypothesis tests breakdown for the problem of comparing two high-dimensional population means due to the singularity of the pooled sample covariance matrices when the model dimension p exceeds the sample size n. In this paper, we develop a simple closed-form Bayesian testing procedure based on a split-and-merge technique. Specifically, we adopt the subspace clustering technique to split the high-dimensional data into lower-dimensional random spaces so that the Bayes factor can be implemented. Then we utilize the geometric mean to merge the results of the Bayesian test to obtain a novel test statistic. We carry out simulation studies to compare the performance of the proposed test with several existing ones in the literature. Finally, two real-data applications are provided for illustrative purposes.

Suggested Citation

  • Fang Chen & Qiuchen Hai & Min Wang, 2024. "Bayesian hypothesis testing for equality of high-dimensional means using cluster subspaces," Computational Statistics, Springer, vol. 39(3), pages 1301-1320, May.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:3:d:10.1007_s00180-023-01366-0
    DOI: 10.1007/s00180-023-01366-0
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    References listed on IDEAS

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    1. Zhang, Huaiyu & Wang, Haiyan, 2021. "A more powerful test of equality of high-dimensional two-sample means," Computational Statistics & Data Analysis, Elsevier, vol. 164(C).
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    3. 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.
    4. Liang, Feng & Paulo, Rui & Molina, German & Clyde, Merlise A. & Berger, Jim O., 2008. "Mixtures of g Priors for Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 410-423, March.
    5. Roger S. Zoh & Abhra Sarkar & Raymond J. Carroll & Bani K. Mallick, 2018. "A Powerful Bayesian Test for Equality of Means in High Dimensions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(524), pages 1733-1741, October.
    6. 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.
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