IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v36y2021i2d10.1007_s00180-020-01030-x.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-020-01030-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-020-01030-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. 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).
    3. 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.
    4. 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.
    5. Yuanyuan Jiang & Xingzhong Xu, 2022. "A Two-Sample Test of High Dimensional Means Based on Posterior Bayes Factor," Mathematics, MDPI, vol. 10(10), pages 1-23, May.
    6. 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).
    7. Ghosh, Santu & Ayyala, Deepak Nag & Hellebuyck, Rafael, 2021. "Two-sample high dimensional mean test based on prepivots," Computational Statistics & Data Analysis, Elsevier, vol. 163(C).
    8. 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).
    9. Zhang, Huaiyu & Wang, Haiyan, 2021. "A more powerful test of equality of high-dimensional two-sample means," Computational Statistics & Data Analysis, Elsevier, vol. 164(C).
    10. Li, Yang & Wang, Zhaojun & Zou, Changliang, 2016. "A simpler spatial-sign-based two-sample test for high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 192-198.
    11. Tzviel Frostig & Yoav Benjamini, 2022. "Testing the equality of multivariate means when $$p>n$$ p > n by combining the Hotelling and Simes tests," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 390-415, June.
    12. 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.
    13. Feng, Long & Sun, Fasheng, 2015. "A note on high-dimensional two-sample test," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 29-36.
    14. Yin, Yanqing, 2021. "Test for high-dimensional mean vector under missing observations," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    15. Li, Jun, 2023. "Finite sample t-tests for high-dimensional means," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    16. Amanda Plunkett & Junyong Park, 2019. "Two-sample test for sparse high-dimensional multinomial distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 804-826, September.
    17. 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.
    18. Jinyuan Chang & Wen Zhou & Wen-Xin Zhou & Lan Wang, 2017. "Comparing large covariance matrices under weak conditions on the dependence structure and its application to gene clustering," Biometrics, The International Biometric Society, vol. 73(1), pages 31-41, March.
    19. Zhao, Junguang & Xu, Xingzhong, 2016. "A generalized likelihood ratio test for normal mean when p is greater than n," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 91-104.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:compst:v:36:y:2021:i:2:d:10.1007_s00180-020-01030-x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.