IDEAS home Printed from https://ideas.repec.org/a/eee/ecosta/v14y2020icp131-144.html
   My bibliography  Save this article

A Simple Scale-Invariant Two-Sample Test for High-dimensional Data

Author

Listed:
  • Zhang, Liang
  • Zhu, Tianming
  • Zhang, Jin-Ting

Abstract

A new scale-invariant test for two-sample problems for high-dimensional data is proposed and studied. Under some regularity conditions and the null hypothesis, the proposed test statistic and a chi-square-type mixture are shown to have the same limiting distribution after they are normalized. The limiting distribution can be normal or non-normal, depending on the underlying covariance structure of the high-dimensional data. To approximate the null distribution of the proposed test, the well-known Welch-Satterthwaite chi-square approximation is applied. The resulting test is shown to be adaptive to the shape of the underlying null distribution in the sense that when the test statistic is asymptotically normally distributed under the null hypothesis, so is the approximation distribution, and when the approximation distribution is asymptotically non-normally distributed, so is the underlying null distribution of the test statistic. The asymptotic powers of the proposed test under some local alternatives are derived. Simulation studies and a real data application are used to demonstrate the good performance of the proposed test compared with several existing competitors in the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ecosta:v:14:y:2020:i:c:p:131-144
    DOI: 10.1016/j.ecosta.2019.12.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S2452306220300010
    Download Restriction: Full text for ScienceDirect subscribers only. Contains open access articles
    File URL: https://libkey.io/10.1016/j.ecosta.2019.12.002?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. 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.
    2. 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.
    3. Jin-Ting Zhang, 2005. "Approximate and Asymptotic Distributions of Chi-Squared-Type Mixtures With Applications," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 273-285, March.
    4. 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.
    5. 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.
    6. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.

    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. 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).
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Yin, Yanqing, 2021. "Test for high-dimensional mean vector under missing observations," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    8. 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.
    9. 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.
    10. Davy Paindaveine & Thomas Verdebout, 2013. "Universal Asymptotics for High-Dimensional Sign Tests," Working Papers ECARES ECARES 2013-40, ULB -- Universite Libre de Bruxelles.
    11. 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.
    12. 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).
    13. Ayyala, Deepak Nag & Park, Junyong & Roy, Anindya, 2017. "Mean vector testing for high-dimensional dependent observations," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 136-155.
    14. 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.
    15. 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.
    16. Feng, Long & Sun, Fasheng, 2015. "A note on high-dimensional two-sample test," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 29-36.
    17. 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.
    18. Feng, Long & Zhang, Xiaoxu & Liu, Binghui, 2020. "A high-dimensional spatial rank test for two-sample location problems," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    19. Muni S. Srivastava & Hirokazu Yanagihara & Tatsuya Kubokawa, 2014. "Tests for Covariance Matrices in High Dimension with Less Sample Size," CIRJE F-Series CIRJE-F-933, CIRJE, Faculty of Economics, University of Tokyo.
    20. Cai, T. Tony & Xia, Yin, 2014. "High-dimensional sparse MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 174-196.

    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:eee:ecosta:v:14:y:2020:i:c:p:131-144. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/econometrics-and-statistics .

    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.