IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v204y2025ics0167947324001804.html
   My bibliography  Save this article

High-dimensional copula-based Wasserstein dependence

Author

Listed:
  • De Keyser, Steven
  • Gijbels, Irène

Abstract

The aim is to generalize 2-Wasserstein dependence coefficients to measure dependence between a finite number of random vectors. This generalization includes theoretical properties, and in particular focuses on an interpretation of maximal dependence and an asymptotic normality result for a proposed semi-parametric estimator under a Gaussian copula assumption. In addition, it is of interest to look at general axioms for dependence measures between multiple random vectors, at plausible normalizations, and at various examples. Afterwards, it is important to study plug-in estimators based on penalized empirical covariance matrices in order to deal with high dimensionality issues and taking possible marginal independencies into account by inducing (block) sparsity. The latter ideas are investigated via a simulation study, considering other dependence coefficients as well. The use of the developed methods is illustrated in two real data applications.

Suggested Citation

  • De Keyser, Steven & Gijbels, Irène, 2025. "High-dimensional copula-based Wasserstein dependence," Computational Statistics & Data Analysis, Elsevier, vol. 204(C).
    • Handle: RePEc:eee:csdana:v:204:y:2025:i:c:s0167947324001804
    DOI: 10.1016/j.csda.2024.108096
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947324001804
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2024.108096?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. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. Warton, David I., 2008. "Penalized Normal Likelihood and Ridge Regularization of Correlation and Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 340-349, March.
    3. Jacob Bien & Robert J. Tibshirani, 2011. "Sparse estimation of a covariance matrix," Biometrika, Biometrika Trust, vol. 98(4), pages 807-820.
    4. Gery Geenens & Pierre Lafaye de Micheaux, 2022. "The Hellinger Correlation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(538), pages 639-653, April.
    5. De Keyser, Steven & Gijbels, Irène, 2024. "Parametric dependence between random vectors via copula-based divergence measures," Journal of Multivariate Analysis, Elsevier, vol. 203(C).
    6. Zhang, Qingzhao & Ma, Shuangge & Huang, Yuan, 2021. "Promote sign consistency in the joint estimation of precision matrices," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    7. Schmid, Friedrich & Schmidt, Rafael, 2007. "Multivariate extensions of Spearman's rho and related statistics," Statistics & Probability Letters, Elsevier, vol. 77(4), pages 407-416, February.
    8. Azadkia, Mona & Chatterjee, Sourav, 2021. "A simple measure of conditional dependence," LSE Research Online Documents on Economics 125584, London School of Economics and Political Science, LSE Library.
    9. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    10. Genest, Christian & Rémillard, Bruno & Beaudoin, David, 2009. "Goodness-of-fit tests for copulas: A review and a power study," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 199-213, April.
    11. Fuchs, Sebastian & Di Lascio, F. Marta L. & Durante, Fabrizio, 2021. "Dissimilarity functions for rank-invariant hierarchical clustering of continuous variables," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    12. Lam, Clifford & Fan, Jianqing, 2009. "Sparsistency and rates of convergence in large covariance matrix estimation," LSE Research Online Documents on Economics 31540, London School of Economics and Political Science, LSE Library.
    13. Mordant, Gilles & Segers, Johan, 2022. "Measuring dependence between random vectors via optimal transport," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    14. Gijbels, Irène & Kika, Vojtěch & Omelka, Marek, 2021. "On the specification of multivariate association measures and their behaviour with increasing dimension," Journal of Multivariate Analysis, Elsevier, vol. 182(C).
    15. Lingyue Zhang & Dawei Lu & Xiaoguang Wang, 2021. "The essential dependence for a group of random vectors," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(24), pages 5836-5872, November.
    16. Shih, Jia-Han & Emura, Takeshi, 2021. "On the copula correlation ratio and its generalization," Journal of Multivariate Analysis, Elsevier, vol. 182(C).
    17. Hofert, Marius & Oldford, Wayne & Prasad, Avinash & Zhu, Mu, 2019. "A framework for measuring association of random vectors via collapsed random variables," Journal of Multivariate Analysis, Elsevier, vol. 172(C), pages 5-27.
    18. Sourav Chatterjee, 2021. "A New Coefficient of Correlation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 2009-2022, October.
    19. Ivan Medovikov & Artem Prokhorov, 2017. "A New Measure of Vector Dependence, with Applications to Financial Risk and Contagion," Journal of Financial Econometrics, Oxford University Press, vol. 15(3), pages 474-503.
    20. Grothe, Oliver & Schnieders, Julius & Segers, Johan, 2014. "Measuring association and dependence between random vectors," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 96-110.
    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. De Keyser, Steven & Gijbels, Irène, 2024. "Parametric dependence between random vectors via copula-based divergence measures," Journal of Multivariate Analysis, Elsevier, vol. 203(C).
    2. Lam, Clifford, 2020. "High-dimensional covariance matrix estimation," LSE Research Online Documents on Economics 101667, London School of Economics and Political Science, LSE Library.
    3. Bailey, Natalia & Pesaran, M. Hashem & Smith, L. Vanessa, 2019. "A multiple testing approach to the regularisation of large sample correlation matrices," Journal of Econometrics, Elsevier, vol. 208(2), pages 507-534.
    4. Vahe Avagyan & Andrés M. Alonso & Francisco J. Nogales, 2018. "D-trace estimation of a precision matrix using adaptive Lasso penalties," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(2), pages 425-447, June.
    5. Wessel N. Wieringen & Gwenaël G. R. Leday, 2024. "Ridge-type covariance and precision matrix estimators of the multivariate normal distribution," Statistical Papers, Springer, vol. 65(9), pages 5835-5849, December.
    6. Benjamin Poignard & Manabu Asai, 2023. "Estimation of high-dimensional vector autoregression via sparse precision matrix," The Econometrics Journal, Royal Economic Society, vol. 26(2), pages 307-326.
    7. Bai, Jushan & Liao, Yuan, 2016. "Efficient estimation of approximate factor models via penalized maximum likelihood," Journal of Econometrics, Elsevier, vol. 191(1), pages 1-18.
    8. Lee, Kyoungjae & Jo, Seongil & Lee, Jaeyong, 2022. "The beta-mixture shrinkage prior for sparse covariances with near-minimax posterior convergence rate," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    9. Mordant, Gilles & Segers, Johan, 2022. "Measuring dependence between random vectors via optimal transport," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    10. Wang, Shaoxin, 2021. "An efficient numerical method for condition number constrained covariance matrix approximation," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    11. Yang, Yihe & Zhou, Jie & Pan, Jianxin, 2021. "Estimation and optimal structure selection of high-dimensional Toeplitz covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    12. Kang, Xiaoning & Kang, Lulu & Chen, Wei & Deng, Xinwei, 2022. "A generative approach to modeling data with quantitative and qualitative responses," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    13. Bai, Jushan & Liao, Yuan, 2012. "Efficient Estimation of Approximate Factor Models," MPRA Paper 41558, University Library of Munich, Germany.
    14. Choi, Young-Geun & Lim, Johan & Roy, Anindya & Park, Junyong, 2019. "Fixed support positive-definite modification of covariance matrix estimators via linear shrinkage," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 234-249.
    15. 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.
    16. F. Durante & A. Gatto & F. Ravazzolo, 2024. "Understanding relationships with the Aggregate Zonal Imbalance using copulas," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 33(2), pages 513-554, April.
    17. Avagyan, Vahe & Alonso Fernández, Andrés Modesto & Nogales, Francisco J., 2015. "D-trace Precision Matrix Estimation Using Adaptive Lasso Penalties," DES - Working Papers. Statistics and Econometrics. WS 21775, Universidad Carlos III de Madrid. Departamento de Estadística.
    18. Gaißer, Sandra & Schmid, Friedrich, 2010. "On testing equality of pairwise rank correlations in a multivariate random vector," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2598-2615, November.
    19. Paola Stolfi & Mauro Bernardi & Lea Petrella, 2016. "Multivariate Method Of Simulated Quantiles," Departmental Working Papers of Economics - University 'Roma Tre' 0212, Department of Economics - University Roma Tre.
    20. Bing-Yi Jing & Zhouping Li & Guangming Pan & Wang Zhou, 2016. "On SURE-Type Double Shrinkage Estimation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1696-1704, October.

    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:204:y:2025:i:c:s0167947324001804. 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.