Test for high-dimensional linear hypothesis of mean vectors via random integration

Jianghao Li (), Shizhe Hong (), Zhenzhen Niu () and Zhidong Bai ()
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Jianghao Li: Northeast Normal University
Shizhe Hong: Shanghai University of Finance and Economics
Zhenzhen Niu: Shandong Normal University
Zhidong Bai: Northeast Normal University

Statistical Papers, 2025, vol. 66, issue 1, No 8, 34 pages

Abstract: Abstract In this paper, we investigate hypothesis testing for the linear combination of mean vectors across multiple populations through the method of random integration. We have established the asymptotic distributions of the test statistics under both null and alternative hypotheses. Additionally, we provide a theoretical explanation for the special use of our test statistics in situations when the nonzero signals in the linear combination of the true mean vectors are weakly dense and nearly the same sign. Moreover, Monte Carlo simulations are presented to evaluate the suggested test against existing high-dimensional tests. The findings from these simulations reveal that our test not only aligns with the performance of other tests in terms of size but also exhibits superior power.

Keywords: High-dimensional data; Linear hypothesis; Mean vector tests; U-statistics; 62H15; 62E20 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00362-024-01624-3

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