IDEAS home Printed from https://ideas.repec.org/a/spr/stmapp/v29y2020i2d10.1007_s10260-019-00477-7.html
   My bibliography  Save this article

Testing the equality of matrix distributions

Author

Listed:
  • Lingzhe Guo

    (The George Washington University)

  • Reza Modarres

    (The George Washington University)

Abstract

While matrices are usually used as the basic data structure for experiments with repeated measurements or longitudinal data, testing methods for the equality of two matrix distributions have not been fully discussed in the literature. In this article, we propose three methods to test the equality of two matrix distributions: the likelihood ratio test, the Frobenius norm methods and triangle tests. We present a simulation to compare their performance under the matrix normal distribution. We apply the testing methods to compare the US economy, as measured by closing prices of five market indices, before and after the US stock market crash of 2008.

Suggested Citation

  • Lingzhe Guo & Reza Modarres, 2020. "Testing the equality of matrix distributions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(2), pages 289-307, June.
    • Handle: RePEc:spr:stmapp:v:29:y:2020:i:2:d:10.1007_s10260-019-00477-7
    DOI: 10.1007/s10260-019-00477-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10260-019-00477-7
    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/s10260-019-00477-7?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. Yin Xia & Lexin Li, 2017. "Hypothesis testing of matrix graph model with application to brain connectivity analysis," Biometrics, The International Biometric Society, vol. 73(3), pages 780-791, September.
    2. 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.
    3. Lovison, Gianfranco, 2006. "A matrix-valued Bernoulli distribution," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1573-1585, August.
    4. Mitchell, Matthew W. & Genton, Marc G. & Gumpertz, Marcia L., 2006. "A likelihood ratio test for separability of covariances," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1025-1043, May.
    5. Vermunt, Jeroen K., 2007. "A hierarchical mixture model for clustering three-way data sets," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5368-5376, July.
    6. 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.
    7. Viroli, Cinzia, 2012. "On matrix-variate regression analysis," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 296-309.
    8. Lu, Nelson & Zimmerman, Dale L., 2005. "The likelihood ratio test for a separable covariance matrix," Statistics & Probability Letters, Elsevier, vol. 73(4), pages 449-457, July.
    9. Dayanand Naik & Shantha Rao, 2001. "Analysis of multivariate repeated measures data with a Kronecker product structured covariance matrix," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(1), pages 91-105.
    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. Manceur, A.M. & Dutilleul, P., 2013. "Unbiased modified likelihood ratio tests for simple and double separability of a variance–covariance structure," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 631-636.
    2. Filipiak, Katarzyna & Klein, Daniel & Roy, Anuradha, 2016. "Score test for a separable covariance structure with the first component as compound symmetric correlation matrix," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 105-124.
    3. Viroli, Cinzia, 2012. "On matrix-variate regression analysis," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 296-309.
    4. Filipiak, Katarzyna & Klein, Daniel, 2017. "Estimation of parameters under a generalized growth curve model," Journal of Multivariate Analysis, Elsevier, vol. 158(C), pages 73-86.
    5. Katarzyna Filipiak & Daniel Klein & Anuradha Roy, 2015. "Score test for a separable covariance structure with the first component as compound symmetric correlation matrix," Working Papers 0148mss, College of Business, University of Texas at San Antonio.
    6. 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.
    7. Guggenberger, Patrik & Kleibergen, Frank & Mavroeidis, Sophocles, 2023. "A test for Kronecker Product Structure covariance matrix," Journal of Econometrics, Elsevier, vol. 233(1), pages 88-112.
    8. Sean L Simpson & Lloyd J Edwards & Martin A Styner & Keith E Muller, 2014. "Kronecker Product Linear Exponent AR(1) Correlation Structures for Multivariate Repeated Measures," PLOS ONE, Public Library of Science, vol. 9(2), pages 1-10, February.
    9. 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.
    10. Timothy Opheim & Anuradha Roy, 2021. "Linear models for multivariate repeated measures data with block exchangeable covariance structure," Computational Statistics, Springer, vol. 36(3), pages 1931-1963, September.
    11. Filipiak, Katarzyna & Klein, Daniel & Mokrzycka, Monika, 2024. "Discrepancy between structured matrices in the power analysis of a separability test," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).
    12. 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.
    13. Kim, Seungkyu & Park, Seongoh & Lim, Johan & Lee, Sang Han, 2023. "Robust tests for scatter separability beyond Gaussianity," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    14. Reza Modarres, 2020. "Graphical Comparison of High‐Dimensional Distributions," International Statistical Review, International Statistical Institute, vol. 88(3), pages 698-714, December.
    15. 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).
    16. Martin Ohlson & Zhanna Andrushchenko & Dietrich Rosen, 2011. "Explicit estimators under m-dependence for a multivariate normal distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(1), pages 29-42, February.
    17. Lovato, Ilenia & Pini, Alessia & Stamm, Aymeric & Vantini, Simone, 2020. "Model-free two-sample test for network-valued data," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    18. Hao, Chengcheng & Liang, Yuli & Mathew, Thomas, 2016. "Testing variance parameters in models with a Kronecker product covariance structure," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 182-189.
    19. Kohli, Priya & Garcia, Tanya P. & Pourahmadi, Mohsen, 2016. "Modeling the Cholesky factors of covariance matrices of multivariate longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 87-100.
    20. Kim, Chulmin & Zimmerman, Dale L., 2012. "Unconstrained models for the covariance structure of multivariate longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 104-118.

    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:stmapp:v:29:y:2020:i:2:d:10.1007_s10260-019-00477-7. 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.