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Estimation procedures for exchangeable Marshall copulas with hydrological application

Author

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  • Durante, Fabrizio
  • Okhrin, Ostap

Abstract

Complex phenomena in environmental sciences can be conveniently represented by several inter-dependent random variables. In order to describe such situations, copula-based models have been studied during the last year. In this paper, we consider a novel family of bivariate copulas, called exchangeable Marshall copulas. Such copulas describe both positive and (upper) tail association between random variables. Speci cally, inference procedures for the family of exchangeable Marshall copulas are introduced, based on the estimation of their (univariate) generator. Moreover, the performance of the proposed methodologies is shown in a simulation study. Finally, an illustration describes how the proposed procedures can be useful in a hydrological application.

Suggested Citation

  • Durante, Fabrizio & Okhrin, Ostap, 2014. "Estimation procedures for exchangeable Marshall copulas with hydrological application," SFB 649 Discussion Papers 2014-014, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2014-014
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    References listed on IDEAS

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    1. Fabrizio Durante, 2009. "Construction of non-exchangeable bivariate distribution functions," Statistical Papers, Springer, vol. 50(2), pages 383-391, March.
    2. Néstor Aguilera & Liliana Forzani & Pedro Morin, 2011. "On uniform consistent estimators for convex regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(4), pages 897-908.
    3. Manner, Hans & Segers, Johan, 2011. "Tails of correlation mixtures of elliptical copulas," LIDAM Reprints ISBA 2011002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Liebscher, Eckhard, 2008. "Construction of asymmetric multivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2234-2250, November.
    5. repec:hal:wpaper:hal-00834000 is not listed on IDEAS
    6. Christian Hering & Jan-Frederik Mai, 2012. "Moment-based estimation of extendible Marshall-Olkin copulas," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(5), pages 601-620, July.
    7. Jean-François Quessy, 2012. "Testing for Bivariate Extreme Dependence Using Kendall's Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(3), pages 497-514, September.
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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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