Simulation techniques of Archimedean Copula Estimators: Parametric and Semi-Parametric Approaches



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Submitted Jun 3, 2021
Published Jul 16, 2021
10.24018/ejmath.2021.2.3.48

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In this paper, we look at two different approaches methodologies for copula estimation. The first is based on a parametric approach using MLE and IFM methods, while the second is entirely based on Kendall's tau and spearman's rho in a semi-parametric context, where the margins are estimated non-parametrically. Interestingly, based on R software simulation techniques, the contribution of their algorithms, approach, and illustration was our main focus for this paper. As an application, a class of Archimedean copulas was notably chosen. This particular class of copulas was also presented for censored data to show the estimator's performance even better.

Keywords: Archimedean copula, Parametric estimation, Simulation study, R software, Semi-parametric approaches

References

  1. Benatia. F & al. A semi parametric estimation procedure for multi parameter Archimedean copulas based on the L-moments method. 2011.Africa statistika, Numero: 335-345.
     Google Scholar
  2. Benatia, F, Chine, A. Bivariate copulas estimation using the trimmes L-moments methode. 2017.Africa Statistika, Numéro: 1185-1197.
     Google Scholar
  3. Brahimi, B et al. A semiparametric estimation of copula models based on the method of moments.2012.Statistical MethodologyVolume 9, Issue 4, July 2012, Pages 467-477.
     Google Scholar
  4. Elamir, E.A.H, SeheultA, H. Trimmed L-moments 2003. Computationalstatistics. Numéro: 299-314.
     Google Scholar
  5. Genest, C and Favre, A. Everything you always wanted to know about copula modeling but were afraid to ask. 2007. Journal of Hydrologic Engineering, 12(4),347–368.
     Google Scholar
  6. Genest, C and Werker, B. J. M. Conditions for the asymptotic semiparametric efficiency of an omnibus estimator of dependence parameters in copula models. In C. M. Cuadras and J. A. R. Lallena, editors, Proceedings of the Conference on Distributions with Given Marginals and Statistical Modelling, pages 103–112, Kluwer Academic Publishers, Dordrecht, 2002.
     Google Scholar
  7. Genest, C, Ghoudi, K. and. Rivest, L. P. A semiparametric estimation procedure of dependence parameters inmultivariate families of distributions. Biometrika, 82(3):543–552, 1995.
     Google Scholar
  8. Genest, C and Rivet, L.-P. (1993). Statistical inference procedures for bivariate Archimedean copulas. Journal of the American Statistical Association 88, 1034–43.
     Google Scholar
  9. Genest, C, MacKay, J (1986). The Joy of Copulas: Bivariate distributions with Uniform Marginals. The American Statistician, 40, 280–283.
     Google Scholar
  10. Kojadinovic, I, Yan, J (2010). Modeling Multivariate Distributions with Continuous Margins Using the copula R Package. Journal of Statistical Software.
     Google Scholar
  11. Lehmann, E. L., & Casella, G. (1998). Theory of point estimation. New York: Springer.
     Google Scholar
  12. Mari, D. D. and S. Kotz (2001). Correlation and Dependence. London: Imperial College Press.
     Google Scholar
  13. Marius, H, Martin, .M, Alexander .J.M. Likelihood inference for Archimedean copulas in high dimensions under known margins. Journal of Multivariate analysis, September 2012.
     Google Scholar
  14. Nelsen R. B., 2006. An Introduction to Copulas, second ed. Springer, New York.
     Google Scholar
  15. Oakes D., 1982. A model for association in bivariate survival data. J. Roy. Statist. Soc. Ser. B 44, no. 3, 414-422.
     Google Scholar
  16. Scarsini M (1984). On Measures of Concordance Stochastica,8(3), 201{218}.
     Google Scholar
  17. Tsukahara, H., 2005. Semiparametric estimation in copula models. Canad. J. Statist. 33, 357-375.
     Google Scholar
  18. Valdez E. A. (2001). Copula Models for Sums of dependent Risks, School of Actuarial Studies, University of New South Wales.
     Google Scholar
  19. Xu. J.J, Statistical Modelling and Inference for Multivariate and Longitudinal Discrete Response Data. Ph.D. Thesis, Department of Statistics, University of British Columbia, 1996.
     Google Scholar
  20. Yan, J (2007). Enjoy the Joy of Copulas: With a Package copula. Journal of Statistical Software.
     Google Scholar
  21. Fermanian, J.-D., & Scaillet, O. (2005). Some statistical pitfalls in copula modelling for financial applications. In E. Klein (Ed.), Capital formation, governance and banking (pp. 59–74). Hauppauge, NY: Nova Science.
     Google Scholar
  22. Kim G., Silvapulle, M. J., & Silvapulle P. (2007). Comparison of semiparametric and parametric methods for estimating copulas. Computational Statistics & Data Analysis, 51(6), 2836–2850.
     Google Scholar
  23. GenestC., 1987. Frank’s family of bivariate distributions. Biometrika, 74, 549-555.
     Google Scholar
  24. Hoeffding, W.A class of statistics with asymptotically normal distribution. The Annals of Mathematical Statistics, 19(3) :293–325, 1948.
     Google Scholar
  25. Hofert, M et al. 2017. Elements of Copula Modeling with R. Springer.
     Google Scholar
  26. Hofert, M. (2008). Sampling Archimedean copulas. Computational Statistics &DataAnalysis,52,5163–5174.
     Google Scholar
  27. Hofert, M (2010). Sampling Nested Archimedean Copulas with Applications to CDO Pricing. N978-3-8381-1656-3. PhD thesis.
     Google Scholar
  28. Joe, H., 2005. Asymptotic efficiency of the two-stage estimation method for copula-based models. J. multivariate Anal. 94, 401-419.
     Google Scholar
  29. Joe, H. 1997. Multivariate Models and Dependence concepts, Chapman & Hall, London.
     Google Scholar
  30. Jouini, M. N. and R. T. Clemen (1996). Copula models for aggregating expert opinions. Operations Research 44, 444–57.
     Google Scholar
  31. Kimberling, CH (1974). A Probabilistic Interpretation of Complete Monotonicity. Aequationes Mathematicae, 10, 152{164}.
     Google Scholar
  32. Klaassen, C. A. J. and J. A. Wellner. Efficient estimation in the bivariate normal copula model: normal margins are least favourable. Bernoulli, 55–77, 1997.
     Google Scholar