IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v179y2023ics0167947322002134.html
   My bibliography  Save this article

Robust tests for scatter separability beyond Gaussianity

Author

Listed:
  • Kim, Seungkyu
  • Park, Seongoh
  • Lim, Johan
  • Lee, Sang Han

Abstract

Separability (a Kronecker product) of a scatter matrix is one of favorable structures when multivariate heavy-tailed data are collected in a matrix form, due to its parsimonious representation. However, little attempt has been made to test separability beyond Gaussianity. In this paper, we present nonparametric separability tests that can be applied to a larger class of multivariate distributions not only including elliptical distributions but also generalized elliptical distributions and transelliptical distributions. The proposed test statistic exploits robustness of Tyler's M (or Kendall's tau) estimator and a likelihood function of a scaled variable. Since its distribution is hard to specify, we approximate the p-value using a permutation procedure, whose unbiasedness is obtained from the permutation invariance of multivariate paired data. Our simulation study demonstrates the efficacy of our method against other alternatives, and we apply it to rhesus monkey data and corpus callosum data.

Suggested Citation

  • 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).
  • Handle: RePEc:eee:csdana:v:179:y:2023:i:c:s0167947322002134
    DOI: 10.1016/j.csda.2022.107633
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947322002134
    Download Restriction: Full text for ScienceDirect subscribers only.

    File URL: https://libkey.io/10.1016/j.csda.2022.107633?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. Jianqing Fan & Yuan Liao & Han Liu, 2016. "An overview of the estimation of large covariance and precision matrices," Econometrics Journal, Royal Economic Society, vol. 19(1), pages 1-32, February.
    2. Fang Han & Han Liu, 2018. "ECA: High-Dimensional Elliptical Component Analysis in Non-Gaussian Distributions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 252-268, January.
    3. 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.
    4. Seongoh Park & Johan Lim & Hyejeong Choi & Minjung Kwak, 2020. "Clustering of longitudinal interval-valued data via mixture distribution under covariance separability," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(10), pages 1739-1756, July.
    5. Niu, Lu & Liu, Xiumin & Zhao, Junlong, 2020. "Robust estimator of the correlation matrix with sparse Kronecker structure for a high-dimensional matrix-variate," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
    6. Soloveychik, I. & Trushin, D., 2016. "Gaussian and robust Kronecker product covariance estimation: Existence and uniqueness," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 92-113.
    7. Fang Han & Han Liu, 2014. "Scale-Invariant Sparse PCA on High-Dimensional Meta-Elliptical Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 275-287, March.
    8. Frahm, Gabriel & Jaekel, Uwe, 2010. "A generalization of Tyler's M-estimators to the case of incomplete data," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 374-393, February.
    9. 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.
    10. 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.
    11. Genevera I. Allen & Robert Tibshirani, 2012. "Inference with transposable data: modelling the effects of row and column correlations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(4), pages 721-743, September.
    12. Lam, Clifford, 2020. "High-dimensional covariance matrix estimation," LSE Research Online Documents on Economics 101667, London School of Economics and Political Science, LSE Library.
    13. Michael Hornstein & Roger Fan & Kerby Shedden & Shuheng Zhou, 2019. "Joint Mean and Covariance Estimation with Unreplicated Matrix-Variate Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 682-696, April.
    14. Seongoh Park & Johan Lim & Xinlei Wang & Sanghan Lee, 2019. "Permutation based testing on covariance separability," Computational Statistics, Springer, vol. 34(2), pages 865-883, June.
    15. Branco, Márcia D. & Dey, Dipak K., 2001. "A General Class of Multivariate Skew-Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 99-113, October.
    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. 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).
    2. Seongoh Park & Johan Lim & Xinlei Wang & Sanghan Lee, 2019. "Permutation based testing on covariance separability," Computational Statistics, Springer, vol. 34(2), pages 865-883, June.
    3. 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.
    4. Zeyu Wu & Cheng Wang & Weidong Liu, 2023. "A unified precision matrix estimation framework via sparse column-wise inverse operator under weak sparsity," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(4), pages 619-648, August.
    5. 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.
    6. 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.
    7. Yu, Long & He, Yong & Zhang, Xinsheng, 2019. "Robust factor number specification for large-dimensional elliptical factor model," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    8. Viroli, Cinzia, 2012. "On matrix-variate regression analysis," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 296-309.
    9. Enrico Bernardi & Matteo Farnè, 2022. "A Log-Det Heuristics for Covariance Matrix Estimation: The Analytic Setup," Stats, MDPI, vol. 5(3), pages 1-11, July.
    10. 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.
    11. Wang, Lili & Paul, Debashis, 2014. "Limiting spectral distribution of renormalized separable sample covariance matrices when p/n→0," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 25-52.
    12. Evan L. Reynolds & Brian C. Callaghan & Michael Gaies & Mousumi Banerjee, 2023. "Regression Trees and Ensemble for Multivariate Outcomes," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 77-109, May.
    13. 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.
    14. 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.
    15. Sven Husmann & Antoniya Shivarova & Rick Steinert, 2019. "Cross-validated covariance estimators for high-dimensional minimum-variance portfolios," Papers 1910.13960, arXiv.org, revised Oct 2020.
    16. Panagiotelis, Anastasios & Smith, Michael, 2010. "Bayesian skew selection for multivariate models," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1824-1839, July.
    17. Dorota Toczydlowska & Gareth W. Peters & Man Chung Fung & Pavel V. Shevchenko, 2017. "Stochastic Period and Cohort Effect State-Space Mortality Models Incorporating Demographic Factors via Probabilistic Robust Principal Components," Risks, MDPI, vol. 5(3), pages 1-77, July.
    18. Samantha Leorato & Maura Mezzetti, 2015. "Spatial Panel Data Model with error dependence: a Bayesian Separable Covariance Approach," CEIS Research Paper 338, Tor Vergata University, CEIS, revised 09 Apr 2015.
    19. Lin, Edward M.H. & Sun, Edward W. & Yu, Min-Teh, 2020. "Behavioral data-driven analysis with Bayesian method for risk management of financial services," International Journal of Production Economics, Elsevier, vol. 228(C).
    20. Reinaldo B. Arellano-Valle & Marc G. Genton, 2010. "Multivariate extended skew-t distributions and related families," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 201-234.

    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:csdana:v:179:y:2023:i:c:s0167947322002134. 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: http://www.elsevier.com/locate/csda .

    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.