Modelado de parejas aleatorias usando cópulas

• GABRIEL ESCARELA ^[1] ; ANGÉLICA HERNÁNDEZ ^[1]
  1. [1] Universidad Autónoma Metropolitana

     Universidad Autónoma Metropolitana

     México

     
• Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 32, Nº. 1, 2009, págs. 33-58
• Idioma: español
• Títulos paralelos:
  • Modelling random couples using copulas
• Enlaces
  • Texto completo
• Dialnet Métricas: 4 Citas
• Resumen
  • español

    Las cópulas se han convertido en una herramienta útil para el modelado multivariado tanto estocástico como estadístico. En este artículo se revisan propiedades fundamentales de las cópulas que permitan caracterizar la estructura de dependencia de familias de distribución bivariadas definidas por la cópula. También se describen algunas clases de cópulas, enfatizando en la importancia de la cópula Gaussiana y la familia Arquimediana. Se resalta la utilidad de las cópulas para el modelado de parejas de variables aleatorias continuas y el de las discretas. La aplicación de la cópula se ilustra con la construcción de modelos de regresión de Markov de primer orden para respuestas no Gaussianas.

  • English

    Copulas have become a useful tool for the multivariate modelling in both stochastics and statistics. In this article, fundamental properties that allow the characterization of the dependence structure of families of the bivariate distributions defined by the copula are reviewed. Also, the importance of both the Gaussian copula and the Archimedean family is emphasized while some classes of copulas are described. The usefulness for modelling either discrete or continuous random couples is highlighted. The construction of first-order Markov regression models for non-Gaussian responses illustrates the application of the copula.

• Referencias bibliográficas
  • Ané, T.,Kharoubi, C.. (2003). `Dependence Structure and Risk Measure´. The Journal of Business. 76. 411-438
  • Barlow, R. E.,Proschan, F.. (1975). Statistical Theory of Reliability and Life Testing. Holt and Rinehart and Winston.
  • Carriere, J. F.. (1995). `Removing Cancer when it is Correlated with other Causes of Death´. Biometrical Journal. 37. 339-350
  • Charpentier, A.,Juri, A.. (2006). `Limiting Dependence Structures for Tail Events, with Applications to Credit Derivatives´. Journal of...
  • Clemen, R. T.,Reilly, T.. (1999). `Correlations and Copulas for Decision and Risk Analysis´. Management Science. 45. 208-224
  • Denuit, M.,Lambert, P.. (2005). `Constraints on Concordance Measures in Bivariate Discrete Data´. Journal of Multivariate Analysis. 93....
  • Dobric, J.,Schmid, F.. (2007). `A goodness of Fit Test for Copulas Based on Rosenblatt's Transformation´. Computational Statistics...
  • Dunn, P. K.,Smyth, G. K.. (1996). `Randomized Quantile Residuals´. Journal of Computational and Graphical Statistics. 5. 236-244
  • Dupuis, D. J.. (2005). `Ozone Concentrations: A Robust Analysis of Multivariate Extremes´. Technometrics. 47. 191-201
  • Embrechts, P.,McNeil, A. J.,Straumann, D.. (2002). Correlation and dependence in risk management: properties and pitfalls. `Risk Management:...
  • Escarela, G.,Carriere, J. F.. (2003). `Fitting Competing Risks with an Assumed Copula´. Statistical Methods in Medical Research. 12. 333-349
  • Escarela, G.,Mena, R. H.,Castillo-Morales, A.. (2006). `A Flexible Class of Parametric Transition Regression Models Based on Copulas:...
  • Escarela, G.,Pérez-Ruiz, L. C.,Bowater, R.. (2009). `A Copula-Based Markov Chain Model for the Analysis of Binary Longitudinal Data´....
  • Frees, E. W.,Valdez, E. A.. (1998). `Understanding Relationships Using Copulas´. North American Actuarial Journal. 2. 1-25
  • Fréchet, M.. (1951). `Sur les Tableaux de Corrélation dont les Marges sont Donnés´. Annales de l'Université de Lyon. 53-773
  • Genest, C.,Favre, A. C.. (2007). `Everything you always wanted to know about Copula Modeling but were afraid to ask´. Journal of Hydrologic...
  • Genest, C.,MacKay, R. J.. (1986). `The Joy of Copulas: Bivariate Distributions with Uniform Marginals´. The American Statistician. 40....
  • Genest, C.,MacKay, R. J.. (1986). `Copules Archimédiennes et Familles de Lois Bidimensionnelles dont les Marges sont Donnés´. The Canadian...
  • Genest, C.,Rivest, L.. (1993). `Statistical Inference Procedures for Bivariate Archimedian Copulas.´. Journal of the American Statistical...
  • Hougaard, P.. (1986). `A Class of Multivariate Failure Time Distributions´. Biometrika. 73. 671-678
  • Huard, D.,Évin, G.,Favre, A. C.. (2006). `Bayesian Copula Selection´. Computational Statistics & Data Analysis. 51. 809-822
  • Ihaka, R.,Gentleman, R.. (1996). `R: A Language for Data Analysis and Graphics´. Journal of Computational and Graphical Statistics. 5....
  • Jan, Y.. (2007). `Enjoy the Joy of Copulas with a Package Copula´. Journal of Statistical Software. 21. 1-21
  • Joe, H.. (1997). Multivariate Models and Dependence Concepts. Chapman & Hall. New York.
  • Klugman, S.,Parsa, R.. (1999). `Fitting Bivariate loss Distributions with Copulas´. Insurance: Mathematics and Economics. 24. 139-148
  • Lehmann, E. L.. (1966). `Some Concepts of Dependence´. Annals of Mathematical Statistics. 37. 1137-1153
  • Nelsen, R. B.. (1999). An Introduction to Copulas. Springer. New York.
  • Nelsen, R.. (1991). `Advances in Probability Distributions with Given Marginals: Beyond the Copulas´. Kluwer. Dordrecht.
  • Oakes, D.. (1989). `Bivariate Survival Models Induced by Frailties´. Journal of the American Statistical Association. 84. 487-493
  • Rodríguez-Lallena, J. A.,Úbeda-Flores, M.. (2004). `A New Class of Bivariate Copulas´. Statistics & Probability Letters. 66. 315-325
  • Rényi, A.. (1959). `On Measures of Dependence´. Acta Mathematica Academiae Scientiarum Hungaricae. 10. 441-451
  • Scarsini, M.. (1984). `On Measures of Concordance´. Stochastica. 8. 201-218
  • Schweizer, B.,Sklar, A.. (1983). Probabilistic Metric Spaces. Dover Publications. New York.
  • Schweizer, B.,Wolff, E. F.. (1981). `On Nonparametric Measures of Dependence for Random Variables´. The Annals of Statistics. 9. 879-885
  • Schäbe, H.. (1997). `Parameter Estimation for a Special Class of Markov Chains´. Statistical Papers. 38. 303-327
  • Sklar, A.. (1959). `Fonctions de Répartition a n Dimensions et Leurs Marges´. Publications de l'Institut Statistique de l'Université...
  • Smith, R. L.. (1989). `Extreme Value Analysis of Environmental Time Series: An Application to Trend Detection in Ground-Level Ozone´....
  • Song, P. X. K.. (2000). `Multivariate Dispersion Models Generated from Gaussian Copula´. Scandinavian Journal of Statistics. 27. 305-320
  • Stephenson, A.. (2002). `Evd: Extreme Value Distributions´. R News. 2. 31-32
  • Wang, W.,Wells, M.. (2000). `Model Selection and Semiparametric Inference for Bivariate Failure-Time Data´. Journal of the American Statistical...
  • Whelan, N.. (2004). `Sampling from Archimedian Copulas´. Quantitative Finance. 4. 339-352
  • Yanagimoto, T.,Okamoto, M.. (1969). `Partial Orderings of Permutations and Monoticity of a Rank Correlation Statistic´. Annals of the...