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Pair Copula Constructions for Multivariate Discrete Data

Author

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  • Anastasios Panagiotelis
  • Claudia Czado
  • Harry Joe

Abstract

Multivariate discrete response data can be found in diverse fields, including econometrics, finance, biometrics, and psychometrics. Our contribution, through this study, is to introduce a new class of models for multivariate discrete data based on pair copula constructions (PCCs) that has two major advantages. First, by deriving the conditions under which any multivariate discrete distribution can be decomposed as a PCC, we show that discrete PCCs attain highly flexible dependence structures. Second, the computational burden of evaluating the likelihood for an m -dimensional discrete PCC only grows quadratically with m . This compares favorably to existing models for which computing the likelihood either requires the evaluation of 2-super- m terms or slow numerical integration methods. We demonstrate the high quality of inference function for margins and maximum likelihood estimates, both under a simulated setting and for an application to a longitudinal discrete dataset on headache severity. This article has online supplementary material.

Suggested Citation

  • Anastasios Panagiotelis & Claudia Czado & Harry Joe, 2012. "Pair Copula Constructions for Multivariate Discrete Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1063-1072, September.
  • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:499:p:1063-1072
    DOI: 10.1080/01621459.2012.682850
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    File URL: http://hdl.handle.net/10.1080/01621459.2012.682850
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    Citations

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    Cited by:

    1. Krämer, Nicole & Brechmann, Eike C. & Silvestrini, Daniel & Czado, Claudia, 2013. "Total loss estimation using copula-based regression models," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 829-839.
    2. repec:eee:apmaco:v:275:y:2016:i:c:p:268-286 is not listed on IDEAS
    3. repec:eee:csdana:v:114:y:2017:i:c:p:130-145 is not listed on IDEAS
    4. Aristidis Nikoloulopoulos & Harry Joe, 2015. "Factor Copula Models for Item Response Data," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 126-150, March.
    5. Calabrese, Raffaella & Degl’Innocenti, Marta & Osmetti, Silvia Angela, 2017. "The effectiveness of TARP-CPP on the US banking industry: A new copula-based approach," European Journal of Operational Research, Elsevier, vol. 256(3), pages 1029-1037.
    6. repec:gam:jrisks:v:4:y:2016:i:1:p:4:d:64467 is not listed on IDEAS
    7. Zilko, Aurelius A. & Kurowicka, Dorota, 2016. "Copula in a multivariate mixed discrete–continuous model," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 28-55.
    8. Edward W. Frees & Gee Lee & Lu Yang, 2016. "Multivariate Frequency-Severity Regression Models in Insurance," Risks, MDPI, Open Access Journal, vol. 4(1), pages 1-36, February.
    9. Erhardt, Tobias Michael & Czado, Claudia & Schepsmeier, Ulf, 2015. "Spatial composite likelihood inference using local C-vines," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 74-88.
    10. Hua, Lei & Joe, Harry, 2017. "Multivariate dependence modeling based on comonotonic factors," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 317-333.
    11. Siem Jan Koopman & Rutger Lit & André Lucas, 2015. "Intraday Stock Price Dependence using Dynamic Discrete Copula Distributions," Tinbergen Institute Discussion Papers 15-037/III/DSF90, Tinbergen Institute.
    12. Hernandez-Alava, Monica & Pudney, Stephen, 2016. "Copula-based modelling of self-reported health states: an application to the use of EQ-5D-3L and EQ-5D-5L in evaluating drug therapies for rheumatic disease," ISER Working Paper Series 2016-04, Institute for Social and Economic Research.
    13. Hobæk Haff, Ingrid & Aas, Kjersti & Frigessi, Arnoldo & Lacal, Virginia, 2016. "Structure learning in Bayesian Networks using regular vines," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 186-208.
    14. Kim, Daeyoung & Kim, Jong-Min & Liao, Shu-Min & Jung, Yoon-Sung, 2013. "Mixture of D-vine copulas for modeling dependence," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 1-19.
    15. Panagiotelis, Anastasios & Czado, Claudia & Joe, Harry & Stöber, Jakob, 2017. "Model selection for discrete regular vine copulas," Computational Statistics & Data Analysis, Elsevier, vol. 106(C), pages 138-152.
    16. repec:eee:jhecon:v:55:y:2017:i:c:p:139-152 is not listed on IDEAS
    17. Brechmann, Eike & Czado, Claudia & Paterlini, Sandra, 2014. "Flexible dependence modeling of operational risk losses and its impact on total capital requirements," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 271-285.
    18. Jakob Stöber & Ulf Schepsmeier, 2013. "Estimating standard errors in regular vine copula models," Computational Statistics, Springer, vol. 28(6), pages 2679-2707, December.

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