IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v65y2024i8d10.1007_s00362-024-01587-5.html
   My bibliography  Save this article

Hotelling $$T^2$$ T 2 test in high dimensions with application to Wilks outlier method

Author

Listed:
  • Reza Modarres

    (George Washington University)

Abstract

We consider the Hotelling $$T^2$$ T 2 test in low sample size, high dimensional setting. We partition the p variables into $$b>1$$ b > 1 blocks of p/b variables and use the union-intersection principle to propose a testing procedure that computes the $$T^2$$ T 2 test in each block. We show that the proposed method is more powerful than Hotelling $$T^2$$ T 2 test. We also consider Wilks method of outlier detection and use the union-intersection principle to search for outliers in blocks of variables. The significance level and the power function of the new test are investigated. We show that the new outlier detection method produces more power compared to Wilks test.

Suggested Citation

  • Reza Modarres, 2024. "Hotelling $$T^2$$ T 2 test in high dimensions with application to Wilks outlier method," Statistical Papers, Springer, vol. 65(8), pages 5203-5218, October.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:8:d:10.1007_s00362-024-01587-5
    DOI: 10.1007/s00362-024-01587-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-024-01587-5
    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/s00362-024-01587-5?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. Biswas, Munmun & Ghosh, Anil K., 2014. "A nonparametric two-sample test applicable to high dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 160-171.
    2. Paul R. Rosenbaum, 2005. "An exact distribution‐free test comparing two multivariate distributions based on adjacency," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(4), pages 515-530, September.
    3. Yujun Wu & Marc G. Genton & Leonard A. Stefanski, 2006. "A Multivariate Two-Sample Mean Test for Small Sample Size and Missing Data," Biometrics, The International Biometric Society, vol. 62(3), pages 877-885, September.
    4. 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.
    5. Shen, Yanfeng & Lin, Zhengyan & Zhu, Jun, 2011. "Shrinkage-based regularization tests for high-dimensional data with application to gene set analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2221-2233, July.
    6. 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.
    7. 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).
    8. Zhenyu Liu & Reza Modarres, 2011. "A triangle test for equality of distribution functions in high dimensions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 605-615.
    9. Reza Modarres, 2022. "Nonparametric tests for detection of high dimensional outliers," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 34(1), pages 206-227, January.
    10. Marco Marozzi & Amitava Mukherjee & Jan Kalina, 2020. "Interpoint distance tests for high-dimensional comparison studies," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(4), pages 653-665, March.
    11. 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.
    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. Dong, Kai & Pang, Herbert & Tong, Tiejun & Genton, Marc G., 2016. "Shrinkage-based diagonal Hotelling’s tests for high-dimensional small sample size data," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 127-142.
    2. Shin-ichi Tsukada, 2019. "High dimensional two-sample test based on the inter-point distance," Computational Statistics, Springer, vol. 34(2), pages 599-615, June.
    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. Xiao Min & Chen Ting & Huang Kunpeng & Ming Ruixing, 2020. "Optimal Estimation for Power of Variance with Application to Gene-Set Testing," Journal of Systems Science and Information, De Gruyter, vol. 8(6), pages 549-564, December.
    5. 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.
    6. Biswas, Munmun & Ghosh, Anil K., 2014. "A nonparametric two-sample test applicable to high dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 160-171.
    7. Mondal, Pronoy K. & Biswas, Munmun & Ghosh, Anil K., 2015. "On high dimensional two-sample tests based on nearest neighbors," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 168-178.
    8. Cai, T. Tony & Xia, Yin, 2014. "High-dimensional sparse MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 174-196.
    9. 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).
    10. Paul, Biplab & De, Shyamal K. & Ghosh, Anil K., 2022. "Some clustering-based exact distribution-free k-sample tests applicable to high dimension, low sample size data," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    11. Zhang, Liang & Zhu, Tianming & Zhang, Jin-Ting, 2020. "A Simple Scale-Invariant Two-Sample Test for High-dimensional Data," Econometrics and Statistics, Elsevier, vol. 14(C), pages 131-144.
    12. Jiang Hu & Zhidong Bai & Chen Wang & Wei Wang, 2017. "On testing the equality of high dimensional mean vectors with unequal covariance matrices," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(2), pages 365-387, April.
    13. Nicolas Städler & Sach Mukherjee, 2017. "Two-sample testing in high dimensions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 225-246, January.
    14. Zongliang Hu & Tiejun Tong & Marc G. Genton, 2019. "Diagonal likelihood ratio test for equality of mean vectors in high‐dimensional data," Biometrics, The International Biometric Society, vol. 75(1), pages 256-267, March.
    15. Yin, Yanqing, 2021. "Test for high-dimensional mean vector under missing observations," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    16. Li, Jun, 2023. "Finite sample t-tests for high-dimensional means," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    17. 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.
    18. 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.
    19. Davy Paindaveine & Thomas Verdebout, 2013. "Universal Asymptotics for High-Dimensional Sign Tests," Working Papers ECARES ECARES 2013-40, ULB -- Universite Libre de Bruxelles.
    20. Liu, Zhi & Xia, Xiaochao & Zhou, Wang, 2015. "A test for equality of two distributions via jackknife empirical likelihood and characteristic functions," Computational Statistics & Data Analysis, Elsevier, vol. 92(C), pages 97-114.

    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:stpapr:v:65:y:2024:i:8:d:10.1007_s00362-024-01587-5. 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.