A scale-invariant test for linear hypothesis of means in high dimensions

Mingxiang Cao (), Ziyang Cheng, Kai Xu and Daojiang He
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Mingxiang Cao: Anhui Normal University
Ziyang Cheng: Anhui Normal University
Kai Xu: Anhui Normal University
Daojiang He: Anhui Normal University

Statistical Papers, 2024, vol. 65, issue 6, No 6, 3477-3497

Abstract: Abstract In this paper, we propose a new scale-invariant test for linear hypothesis of mean vectors with heteroscedasticity in high-dimensional settings. Most existing tests impose strong conditions on covariance matrices so that null distributions of their tests are asymptotically normal, which restricts the application of test procedures. However, our proposed test has different null distributions under mild conditions. Additionally, the well-known Welch-Satterthwaite chi-square approximation we adopted can automatically mimic the shapes of the null distributions of the test statistic. The performances of the test are illustrated by simulation and real data in finite samples which show that it has robustness and is more powerful than three competitors.

Keywords: Linear hypothesis; Scale-invariant test; $$\chi ^{2}$$ χ 2 -type mixture; High-dimensional data; Primary 62H15; secondary 62E20 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-024-01530-8

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