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Novel multiplier bootstrap tests for high-dimensional data with applications to MANOVA

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  • Chakraborty, Nilanjan
  • Sakhanenko, Lyudmila

Abstract

New bootstrap tests are proposed for linear hypotheses testing of high-dimensional means. In particular, they handle multiple-sample one- and two-way MANOVA tests with unequal cell sizes and unequal unknown cell covariances, as well as contrast tests in elegant and unified way. New tests are compared theoretically and on simulations studies with existing popular contemporary tests. They enjoy consistency, computational efficiency, very mild moment/tail conditions. They avoid the estimation of correlation or precision matrices, and allow the dimension to grow with sample size exponentially. Additionally, they allow the number of groups and the sparsity to grow with the sample size exponentially, thus broadening their applicability.

Suggested Citation

  • Chakraborty, Nilanjan & Sakhanenko, Lyudmila, 2023. "Novel multiplier bootstrap tests for high-dimensional data with applications to MANOVA," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    • Handle: RePEc:eee:csdana:v:178:y:2023:i:c:s0167947322001992
    DOI: 10.1016/j.csda.2022.107619
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    References listed on IDEAS

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    1. Schott, James R., 2007. "Some high-dimensional tests for a one-way MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1825-1839, October.
    2. Cai, T. Tony & Xia, Yin, 2014. "High-dimensional sparse MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 174-196.
    3. Zhang, Jin-Ting & Guo, Jia & Zhou, Bu, 2017. "Linear hypothesis testing in high-dimensional one-way MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 200-216.
    4. Watanabe, Hiroki & Hyodo, Masashi & Nakagawa, Shigekazu, 2020. "Two-way MANOVA with unequal cell sizes and unequal cell covariance matrices in high-dimensional settings," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    5. Zhang, Yi-Chen & Sakhanenko, Lyudmila, 2019. "The naive Bayes classifier for functional data," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 137-146.
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    Keywords

    Bootstrap; MANOVA; GLHT;
    All these keywords.

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