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

Author

Listed:
  • Mingxiang Cao

    (Anhui Normal University)

  • Ziyang Cheng

    (Anhui Normal University)

  • Kai Xu

    (Anhui Normal University)

  • Daojiang He

    (Anhui Normal University)

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.

Suggested Citation

  • Mingxiang Cao & Ziyang Cheng & Kai Xu & Daojiang He, 2024. "A scale-invariant test for linear hypothesis of means in high dimensions," Statistical Papers, Springer, vol. 65(6), pages 3477-3497, August.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:6:d:10.1007_s00362-024-01530-8
    DOI: 10.1007/s00362-024-01530-8
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    References listed on IDEAS

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