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Simulation‐based hypothesis testing of high dimensional means under covariance heterogeneity

Author

Listed:
  • Jinyuan Chang
  • Chao Zheng
  • Wen‐Xin Zhou
  • Wen Zhou

Abstract

In this article, we study the problem of testing the mean vectors of high dimensional data in both one‐sample and two‐sample cases. The proposed testing procedures employ maximum‐type statistics and the parametric bootstrap techniques to compute the critical values. Different from the existing tests that heavily rely on the structural conditions on the unknown covariance matrices, the proposed tests allow general covariance structures of the data and therefore enjoy wide scope of applicability in practice. To enhance powers of the tests against sparse alternatives, we further propose two‐step procedures with a preliminary feature screening step. Theoretical properties of the proposed tests are investigated. Through extensive numerical experiments on synthetic data sets and an human acute lymphoblastic leukemia gene expression data set, we illustrate the performance of the new tests and how they may provide assistance on detecting disease‐associated gene‐sets. The proposed methods have been implemented in an R‐package HDtest and are available on CRAN.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:biomet:v:73:y:2017:i:4:p:1300-1310
    DOI: 10.1111/biom.12695
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    References listed on IDEAS

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    1. 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.
    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.
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    Cited by:

    1. Chang, Jinyuan & Cheng, Guanghui & Yao, Qiwei, 2022. "Testing for unit roots based on sample autocovariances," LSE Research Online Documents on Economics 114620, London School of Economics and Political Science, LSE Library.
    2. He, Yong & Zhang, Mingjuan & Zhang, Xinsheng & Zhou, Wang, 2020. "High-dimensional two-sample mean vectors test and support recovery with factor adjustment," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).
    3. Jinyuan Chang & Guanghui Cheng & Qiwei Yao, 2022. "Testing for unit roots based on sample autocovariances [Heteroskedasticity and autocorrelation consistent covariance matrix estimation]," Biometrika, Biometrika Trust, vol. 109(2), pages 543-550.
    4. 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.
    5. Chang, Jinyuan & Qiu, Yumou & Yao, Qiwei & Zou, Tao, 2018. "Confidence regions for entries of a large precision matrix," Journal of Econometrics, Elsevier, vol. 206(1), pages 57-82.
    6. Chang, Jinyuan & Qiu, Yumou & Yao, Qiwei & Zou, Tao, 2018. "Confidence regions for entries of a large precision matrix," LSE Research Online Documents on Economics 87513, London School of Economics and Political Science, LSE Library.
    7. Chang, Jinyuan & Jiang, Qing & Shao, Xiaofeng, 2023. "Testing the martingale difference hypothesis in high dimension," Journal of Econometrics, Elsevier, vol. 235(2), pages 972-1000.
    8. Huang, Yuan & Li, Changcheng & Li, Runze & Yang, Songshan, 2022. "An overview of tests on high-dimensional means," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    9. Saha, Enakshi & Sarkar, Soham & Ghosh, Anil K., 2017. "Some high-dimensional one-sample tests based on functions of interpoint distances," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 83-95.
    10. Victor Chernozhukov & Denis Chetverikov & Kengo Kato & Yuta Koike, 2022. "High-dimensional Data Bootstrap," Papers 2205.09691, arXiv.org.
    11. Baek, Changryong & Gates, Katheleen M. & Leinwand, Benjamin & Pipiras, Vladas, 2021. "Two sample tests for high-dimensional autocovariances," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).

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