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Two-sample mean vector projection test in high-dimensional data

Author

Listed:
  • Caizhu Huang

    (University of Padova)

  • Xia Cui

    (Guangzhou University)

  • Euloge Clovis Kenne Pagui

    (University of Oslo)

Abstract

Statistical hypothesis testing for high-dimensional data poses challenges in recent inference. The Hotelling test is commonly applied to the comparison of mean vectors with a fixed dimension of mean vectors, but becomes unavailable when the dimension diverges or greater than sample sizes. For the high-dimensional regimes, we propose a two-sample mean vector test statistic by adding a projection term based on the Euclidean norm of the mean vectors. The projection term improves power and ensures the validity for dimensions greater than sample sizes, without relying on any inverse matrices. The proposed projection statistic, suitably standardized, approximates a standard normal distribution under mild conditions. Extensive simulation results, under different scenarios, show that the proposed approach enjoys a comparable Type I error and an improved efficiency power. We further illustrate its application by testing the equality of two acute lymphocytic leukemia genetic data and a significant test of the “Sell in May and Go Away” effect in China A stock market.

Suggested Citation

  • Caizhu Huang & Xia Cui & Euloge Clovis Kenne Pagui, 2024. "Two-sample mean vector projection test in high-dimensional data," Computational Statistics, Springer, vol. 39(3), pages 1061-1091, May.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:3:d:10.1007_s00180-023-01374-0
    DOI: 10.1007/s00180-023-01374-0
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    References listed on IDEAS

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    1. Deepak Nag Ayyala & Santu Ghosh & Daniel F. Linder, 2022. "Covariance matrix testing in high dimension using random projections," Computational Statistics, Springer, vol. 37(3), pages 1111-1141, July.
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    3. Xia Cui & Runze Li & Guangren Yang & Wang Zhou, 2020. "Empirical likelihood test for a large-dimensional mean vector," Biometrika, Biometrika Trust, vol. 107(3), pages 591-607.
    4. Takayuki Yamada & Tetsuto Himeno, 2019. "Estimation of multivariate 3rd moment for high-dimensional data and its application for testing multivariate normality," Computational Statistics, Springer, vol. 34(2), pages 911-941, June.
    5. Jin-Ting Zhang & Jia Guo & Bu Zhou & Ming-Yen Cheng, 2020. "A Simple Two-Sample Test in High Dimensions Based on L2-Norm," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(530), pages 1011-1027, April.
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    7. Chen, Song Xi & Qin, Yingli, 2010. "A Two Sample Test for High Dimensional Data with Applications to Gene-set Testing," MPRA Paper 59642, University Library of Munich, Germany.
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