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Two-way MANOVA with unequal cell sizes and unequal cell covariance matrices in high-dimensional settings

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  • Watanabe, Hiroki
  • Hyodo, Masashi
  • Nakagawa, Shigekazu

Abstract

In this paper, we discuss a two-way multivariate analysis of variance in high-dimensional settings. With a high-dimensional setting, we propose new approximate tests that work well under the following conditions: 1. The error vectors do not necessarily follow a multivariate normal distribution, 2. The cell sizes are unequal, 3. The cell covariance matrices are unequal, and 4. The dimension p is much larger than the total cell size n. The accuracy of the proposed tests with finite samples is shown through simulations for a variety of high-dimensional scenarios.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:jmvana:v:179:y:2020:i:c:s0047259x19303082
    DOI: 10.1016/j.jmva.2020.104625
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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. Srivastava, Muni S. & Fujikoshi, Yasunori, 2006. "Multivariate analysis of variance with fewer observations than the dimension," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 1927-1940, October.
    3. Solomon Harrar & Arne Bathke, 2012. "A modified two-factor multivariate analysis of variance: asymptotics and small sample approximations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(1), pages 135-165, February.
    4. Konietschke, Frank & Bathke, Arne C. & Harrar, Solomon W. & Pauly, Markus, 2015. "Parametric and nonparametric bootstrap methods for general MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 291-301.
    5. Srivastava, Muni S. & Kubokawa, Tatsuya, 2013. "Tests for multivariate analysis of variance in high dimension under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 204-216.
    6. 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.
    7. Hyodo, Masashi & Watanabe, Hiroki & Seo, Takashi, 2018. "On simultaneous confidence interval estimation for the difference of paired mean vectors in high-dimensional settings," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 160-173.
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    Cited by:

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    3. 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).
    4. Abbas, Khizar & Xie, Xiaoqing & Xu, Deyi & Butt, Khalid Manzoor, 2021. "Assessing an empirical relationship between energy poverty and domestic health issues: A multidimensional approach," Energy, Elsevier, vol. 221(C).

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