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Estimation of multivariate critical layers: Applications to rainfall data

Author

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  • Elena Di Bernardino

    (CEDRIC - Centre d'études et de recherche en informatique et communications - ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise - CNAM - Conservatoire National des Arts et Métiers [CNAM])

  • Didier Rullière

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

Abstract

Calculating return periods and critical layers (i.e., multivariate quantile curves) in a multivariate environment is a di cult problem. A possible consistent theoretical framework for the calculation of the return period, in a multi-dimensional environment, is essentially based on the notion of copula and level sets of the multivariate probability distribution. In this paper we propose a fast and parametric methodology to estimate the multivariate critical layers of a distribution and its associated return periods. The model is based on transformations of the marginal distributions and transformations of the dependence structure within the class of Archimedean copulas. The model has a tunable number of parameters, and we show that it is possible to get a competitive estimation without any global optimum research. We also get parametric expressions for the critical layers and return periods. The methodology is illustrated on hydrological 5-dimensional real data. On this real data-set we obtain a good quality of estimation and we compare the obtained results with some classical parametric competitors

Suggested Citation

  • Elena Di Bernardino & Didier Rullière, 2015. "Estimation of multivariate critical layers: Applications to rainfall data," Post-Print hal-00940089, HAL.
    • Handle: RePEc:hal:journl:hal-00940089
    Note: View the original document on HAL open archive server: https://hal.science/hal-00940089v3
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    References listed on IDEAS

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    6. Di Bernardino, Elena & Rullière, Didier, 2013. "Distortions of multivariate distribution functions and associated level curves: Applications in multivariate risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 190-205.
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    8. Di Bernardino Elena & Rullière Didier, 2013. "On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators," Dependence Modeling, De Gruyter, vol. 1(2013), pages 1-36, October.
    9. Christian Genest & Johanna Nešlehová & Johanna Ziegel, 2011. "Rejoinder on: Inference in multivariate Archimedean copula models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 290-292, August.
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    Cited by:

    1. Elena Di Bernardino & Didier Rullière, 2017. "A note on upper-patched generators for Archimedean copulas," Post-Print hal-01347869, HAL.
    2. Elena Di Bernardino & Didier Rullière, 2016. "A note on upper-patched generators for Archimedean copulas," Working Papers hal-01347869, HAL.

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