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Likelihood inference for Archimedean copulas in high dimensions under known margins

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  • Hofert, Marius
  • Mächler, Martin
  • McNeil, Alexander J.

Abstract

Explicit functional forms for the generator derivatives of well-known one-parameter Archimedean copulas are derived. These derivatives are essential for likelihood inference as they appear in the copula density, conditional distribution functions, and the Kendall distribution function. They are also required for several asymmetric extensions of Archimedean copulas such as Khoudraji-transformed Archimedean copulas. Availability of the generator derivatives in a form that permits fast and accurate computation makes maximum-likelihood estimation for Archimedean copulas feasible, even in large dimensions. It is shown, by large scale simulation of the performance of maximum likelihood estimators under known margins, that the root mean squared error actually decreases with both dimension and sample size at a similar rate. Confidence intervals for the parameter vector are derived under known margins. Moreover, extensions to multi-parameter Archimedean families are given. All presented methods are implemented in the R package nacopula and can thus be studied in detail.

Suggested Citation

  • Hofert, Marius & Mächler, Martin & McNeil, Alexander J., 2012. "Likelihood inference for Archimedean copulas in high dimensions under known margins," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 133-150.
  • Handle: RePEc:eee:jmvana:v:110:y:2012:i:c:p:133-150
    DOI: 10.1016/j.jmva.2012.02.019
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    References listed on IDEAS

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    7. Cooray Kahadawala, 2018. "Strictly Archimedean copulas with complete association for multivariate dependence based on the Clayton family," Dependence Modeling, De Gruyter, vol. 6(1), pages 1-18, February.
    8. Woraphon Yamaka & Rangan Gupta & Sukrit Thongkairat & Paravee Maneejuk, 2021. "Structural and Predictive Analyses with a Mixed Copula-Based Vector Autoregression Model," Working Papers 202108, University of Pretoria, Department of Economics.
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