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Nonparametric estimation of the tree structure of a nested Archimedean copula

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  • Segers, Johan
  • Uyttendaele, Nathan

Abstract

One of the features inherent in nested Archimedean copulas, also called hierarchical Archimedean copulas, is their rooted tree structure. A nonparametric, rank-based method to estimate this structure is presented. The idea is to represent the target structure as a set of trivariate structures, each of which can be estimated individually with ease. Indeed, for any three variables there are only four possible rooted tree structures and, based on a sample, a choice can be made by performing comparisons between the three bivariate margins of the empirical distribution of the three variables. The set of estimated trivariate structures can then be used to build an estimate of the target structure. The advantage of this estimation method is that it does not require any parametric assumptions concerning the generator functions at the nodes of the tree.

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  • Segers, Johan & Uyttendaele, Nathan, 2014. "Nonparametric estimation of the tree structure of a nested Archimedean copula," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 190-204.
    • Handle: RePEc:eee:csdana:v:72:y:2014:i:c:p:190-204
    DOI: 10.1016/j.csda.2013.10.028
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    References listed on IDEAS

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    Cited by:

    1. Górecki J. & Hofert M. & Holeňa M., 2017. "Kendall’s tau and agglomerative clustering for structure determination of hierarchical Archimedean copulas," Dependence Modeling, De Gruyter, vol. 5(1), pages 75-87, January.
    2. Uyttendaele, Nathan, 2016. "On the estimation of nested Archimedean copulas: A theoretical and an experimental comparison," LIDAM Discussion Papers ISBA 2016005, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Benjamin Poignard & Jean-David Fermanian, 2022. "The finite sample properties of sparse M-estimators with pseudo-observations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(1), pages 1-31, February.
    4. Cossette, Hélène & Gadoury, Simon-Pierre & Marceau, Étienne & Mtalai, Itre, 2017. "Hierarchical Archimedean copulas through multivariate compound distributions," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 1-13.
    5. Ostap Okhrin & Anastasija Tetereva, 2017. "The Realized Hierarchical Archimedean Copula in Risk Modelling," Econometrics, MDPI, vol. 5(2), pages 1-31, June.
    6. Benjamin Poignard & Jean-David Fermanian, 2019. "The finite sample properties of Sparse M-estimators with Pseudo-Observations," Working Papers 2019-01, Center for Research in Economics and Statistics.
    7. Nathan Uyttendaele, 2018. "On the estimation of nested Archimedean copulas: a theoretical and an experimental comparison," Computational Statistics, Springer, vol. 33(2), pages 1047-1070, June.
    8. Mai Jan-Frederik, 2019. "Simulation algorithms for hierarchical Archimedean copulas beyond the completely monotone case," Dependence Modeling, De Gruyter, vol. 7(1), pages 202-214, January.
    9. Vettori, Sabrina & Huser, Raphael & Segers, Johan & Genton, Marc, 2017. "Bayesian Clustering and Dimension Reduction in Multivariate Extremes," LIDAM Discussion Papers ISBA 2017017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Górecki, Jan & Hofert, Marius & Okhrin, Ostap, 2021. "Outer power transformations of hierarchical Archimedean copulas: Construction, sampling and estimation," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    11. Elena Di Bernardino & Didier Rullière, 2015. "Estimation of multivariate critical layers: Applications to rainfall data," Post-Print hal-00940089, HAL.
    12. Mazo, Gildas & Uyttendaele, Nathan, 2016. "Building conditionally dependent parametric one-factor copulas," LIDAM Discussion Papers ISBA 2016004, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    13. Jean-David Fermanian, 2017. "Recent Developments in Copula Models," Econometrics, MDPI, vol. 5(3), pages 1-3, July.

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