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A stationary bootstrap test about two mean vectors comparison with somewhat dense differences and fewer sample size than dimension

Author

Listed:
  • Zhengbang Li

    (Central China Normal University)

  • Fuxiang Liu

    (China Three Gorges University)

  • Luanjie Zeng

    (Central China Normal University)

  • Guoxin Zuo

    (Central China Normal University)

Abstract

Two sample mean vectors comparison hypothesis testing problems often emerge in modern biostatistics. Many tests are proposed for detecting relatively dense signals with somewhat dense nonzero components in mean vectors differences. One kind of these tests is based on some quadratic forms about two sample mean vectors differences. Another kind of these tests is based on some quadratic forms about studentized version of two sample mean vectors differences. In this article, we propose a bootstrap test by adopting stationary bootstrap scheme to calculate p value of a typical test which is based on a quadratic form about studentized version of two sample mean vectors differences. Extensive simulations are conducted to compare performances of the bootstrap test with other existing typical tests. We also apply the bootstrap test to a real genetic data analysis about breast cancer.

Suggested Citation

  • Zhengbang Li & Fuxiang Liu & Luanjie Zeng & Guoxin Zuo, 2021. "A stationary bootstrap test about two mean vectors comparison with somewhat dense differences and fewer sample size than dimension," Computational Statistics, Springer, vol. 36(2), pages 941-960, June.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:2:d:10.1007_s00180-020-01030-x
    DOI: 10.1007/s00180-020-01030-x
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    References listed on IDEAS

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    1. Tony Cai & Weidong Liu & Yin Xia, 2013. "Two-Sample Covariance Matrix Testing and Support Recovery in High-Dimensional and Sparse Settings," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 265-277, March.
    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.
    3. T. Tony Cai & Weidong Liu & Yin Xia, 2014. "Two-sample test of high dimensional means under dependence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(2), pages 349-372, March.
    4. Jinyuan Chang & Chao Zheng & Wen‐Xin Zhou & Wen Zhou, 2017. "Simulation‐based hypothesis testing of high dimensional means under covariance heterogeneity," Biometrics, The International Biometric Society, vol. 73(4), pages 1300-1310, December.
    5. 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.
    6. Dimitris Politis & Halbert White, 2004. "Automatic Block-Length Selection for the Dependent Bootstrap," Econometric Reviews, Taylor & Francis Journals, vol. 23(1), pages 53-70.
    7. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2012. "Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors," Papers 1212.6906, arXiv.org, revised Jan 2018.
    8. Karl Bruce Gregory & Raymond J. Carroll & Veerabhadran Baladandayuthapani & Soumendra N. Lahiri, 2015. "A Two-Sample Test for Equality of Means in High Dimension," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 837-849, June.
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