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Test on the linear combinations of mean vectors in high-dimensional data

Author

Listed:
  • Huiqin Li

    (Jiangsu Normal University)

  • Jiang Hu

    (Northeast Normal University)

  • Zhidong Bai

    (Northeast Normal University)

  • Yanqing Yin

    (Jiangsu Normal University)

  • Kexin Zou

    (Northeast Normal University)

Abstract

In this study, we propose a procedure for simultaneous testing $$l (l\ge 1)$$ l ( l ≥ 1 ) linear relations on $$k(k\ge 2)$$ k ( k ≥ 2 ) high-dimensional mean vectors with heterogeneous covariance matrices, which extends the result derived by Nishiyama et al. (J Stat Plan Inference 143(11):1898–1911, 2013) and does not need the normality assumption. The newly proposed test statistic is motivated by Bai and Saranadasa (Statistica Sinica 6(2):311–329, 1996) and Chen and Qin (Ann Stat 38(2):808–835, 2010). As a special case, our result could be applied to multivariate analysis of variance, that is, testing the equality of k high-dimensional mean vectors.

Suggested Citation

  • Huiqin Li & Jiang Hu & Zhidong Bai & Yanqing Yin & Kexin Zou, 2017. "Test on the linear combinations of mean vectors in high-dimensional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 188-208, March.
    • Handle: RePEc:spr:testjl:v:26:y:2017:i:1:d:10.1007_s11749-016-0505-3
    DOI: 10.1007/s11749-016-0505-3
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    References listed on IDEAS

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    1. Srivastava, Muni S., 2009. "A test for the mean vector with fewer observations than the dimension under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 518-532, March.
    2. Chen, Songxi, 2012. "Two Sample Tests for High Dimensional Covariance Matrices," MPRA Paper 46026, University Library of Munich, Germany.
    3. 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.
    4. 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.
    5. 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.
    6. Cai, T. Tony & Xia, Yin, 2014. "High-dimensional sparse MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 174-196.
    7. 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.
    8. Srivastava, Muni S. & Du, Meng, 2008. "A test for the mean vector with fewer observations than the dimension," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 386-402, March.
    9. Srivastava, Muni S. & Katayama, Shota & Kano, Yutaka, 2013. "A two sample test in high dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 349-358.
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    Cited by:

    1. Mingxiang Cao & Yuanjing He, 2022. "A high-dimensional test on linear hypothesis of means under a low-dimensional factor model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(5), pages 557-572, July.
    2. 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.
    3. Zhidong Bai & Jiang Hu & Chen Wang & Chao Zhang, 2021. "Test on the linear combinations of covariance matrices in high-dimensional data," Statistical Papers, Springer, vol. 62(2), pages 701-719, April.

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