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Testing homogeneity of mean vectors under heteroscedasticity in high-dimension

Author

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  • Yamada, Takayuki
  • Himeno, Tetsuto

Abstract

This paper is concerned with the problem of testing the homogeneity of mean vectors. The testing problem is without assuming common covariance matrix. We proposed a testing statistic based on the variation matrix due to the hypothesis and the unbiased estimator of the covariance matrix. The limiting null and non-null distributions are derived as each sample size and the dimensionality go to infinity together under a general population distribution, which includes elliptical distribution with finite fourth moments or distribution assumed in Chen and Qin (2010). In two-sample case, our proposed test has the same asymptotic power as Chen and Qin (2010)’s test. In addition, it is found that our proposed test has the same asymptotic power as the one of Dempster’s trace statistic for MANOVA proposed in Fujikoshi et al. (2004) for the case that the population distributions are multivariate normal with common covariance matrix for all groups. A small scale simulation study is performed to compare the actual error probability of the first kind with the nominal.

Suggested Citation

  • Yamada, Takayuki & Himeno, Tetsuto, 2015. "Testing homogeneity of mean vectors under heteroscedasticity in high-dimension," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 7-27.
    • Handle: RePEc:eee:jmvana:v:139:y:2015:i:c:p:7-27
    DOI: 10.1016/j.jmva.2015.02.005
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    References listed on IDEAS

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    1. 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.
    2. 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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    Citations

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    Cited by:

    1. 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.
    2. Tianming Zhu & Jin-Ting Zhang, 2022. "Linear hypothesis testing in high-dimensional one-way MANOVA: a new normal reference approach," Computational Statistics, Springer, vol. 37(1), pages 1-27, March.
    3. Zhang, Jin-Ting & Zhu, Tianming, 2022. "A new normal reference test for linear hypothesis testing in high-dimensional heteroscedastic one-way MANOVA," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    4. Pini, Alessia & Stamm, Aymeric & Vantini, Simone, 2018. "Hotelling’s T2 in separable Hilbert spaces," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 284-305.
    5. Lixiu Wu & Jiang Hu, 2024. "Multi-sample hypothesis testing of high-dimensional mean vectors under covariance heterogeneity," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(4), pages 579-615, August.
    6. Zhang, Jin-Ting & Zhou, Bu & Guo, Jia, 2022. "Linear hypothesis testing in high-dimensional heteroscedastic one-way MANOVA: A normal reference L2-norm based test," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    7. Zhou, Bu & Guo, Jia, 2017. "A note on the unbiased estimator of Σ2," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 141-146.
    8. 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.
    9. Harrar, Solomon W. & Kong, Xiaoli, 2022. "Recent developments in high-dimensional inference for multivariate data: Parametric, semiparametric and nonparametric approaches," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    10. Jin-Ting Zhang & Bu Zhou & Jia Guo, 2022. "Testing high-dimensional mean vector with applications," Statistical Papers, Springer, vol. 63(4), pages 1105-1137, August.

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