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

Fang Chen, Qiuchen Hai and Min Wang ()
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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

Computational Statistics, 2024, vol. 39, issue 3, No 9, 1320 pages

Abstract: 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.

Keywords: Bayes factor; High-dimensional data; Hierarchical clustering; Large p small n (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00180-023-01366-0

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