ESTIMATION USING COPULA FUNCTION IN REGRESSION MODEL

ESTIMATION USING COPULA FUNCTION IN REGRESSION MODEL

Copula models are becoming an increasingly powerful tool formodeling the dependencies between random variables, they have useful applications in many fields such as biostatistics, actuarial science, and finance.In this paper, we investigate the estimate of a regression model, by use of thecopula representation. Its asymptotic properties are studied; almost surelyconvergence and convergence in probability (with rate)
Keywords:

-,

___

  • Biau,G., AND Wegkamp,M.H.,” A note on minimum distance estimation of copulas densi- ties”., Statist. Probab. Lett., No.73, (2006), pp. 105-114.
  • Bosq, D., Nonparametric statistics for stochastic processes, second ed., Vol. 110 of Lecture Notes in Statistics. Springer-Verlag, New York, (1998). Estimation and prediction.
  • Cherubini, U., Luciano, E., AND Vecchiato, W., Copula Methods in Finance. John Wiley and Sons, Chichester (2004). [4] Deheuvels, P., ”La fonction de d´ependance empirique et ses propri´et´es. Un test non param´etrique d’ind´ependance”. Acad. Roy. Belg. Bull. Cl. Sci., Vol.65,No.5 And 6, (1979),pp. 274-292.
  • Deheuvels, P., ”A Kolmogorov-Smirnov type test for independence and multivariate samples”, Rev. Roumaine Math. Pures Appl.Vol 26,No.2, (1981), pp. 213-226.
  • Embrechts, P., Lindskog, F., McNeil, A., Modelling dependence with copulas and applications to risk management., Handbook of Heavey Tailed Distributions in Finance, S.T. Rachev (ed.). Elsevier, Amsterdam (2003). [7] Faugeras, Olivier Paul., Contributions `a la pr´evision statistique, Th`eses de doctorat de l’universit´e Pierre er Marie Curie, 28 Novembre 2008.
  • Fermanian, J.D., ”Goodness-of-fit tests for copulas.”, J. Multivariate Anal. Vol.95, No.1, (2005), pp. 119-152.
  • Fermanian, J.D., Radulov¨ıc, D., AND Wegkamp, M., ”Weak convergence of empirical copula processes”. Bernoulli Vol.10,No.5, (2004), pp. 847-860.
  • Fermanian, J.D., AND Scaillet, O., Some statistical pitfalls in copula modelling for financical applications, E. Klein (Ed.), Capital formation, Gouvernance and Banking. Nova Science Publishing, New York, (2005).
  • Fermanian, J.D.,AND Scaillet, O., ”Nonparametric estimation of copulas for time series”, Journal of Risk, Vol.5,No. 4, (2003), pp. 25-54.
  • Ferraty, F., AND Vieu, P., Nonparametric functional data analysis. Springer Series in Sta- tistics. Springer, New York, (2006). Theory and practice.
  • Fisher, N.I., Copulas, Encyclopedia of Statistical Sciences, Updated Volume 1, S. Kotz, C. B. Read, D. L. Banks (eds.), pp. 159164. John Wiley and Sons, New York (1997).
  • Gijbels, I., AND Mielniczuk, J., ”Estimating the density of a copula function”, Comm. Statist. Theory Methods ,Vol.19,No.2 (1990), pp.445-464.
  • Hutchinson, T.P., Lai, C.D., Continuous Bivariate Distributions: Emphasising Applica- tions,Rumsby Scientific Publishing, Adelaide (1990).
  • Joe, H., Multivariate Models and Dependence Concepts, Chapman and Hall, London (1997). [17] Joe, H., Multivariate models and dependence concepts, vol. 73 of Monographs on Statistics and Applied Probability. Chapman & Hall, London, (1997).
  • Mikosch, T., ”Copulas: Taies and facts”, Extrmes,Vol. 9,No.18,(2006), pp.3-22 .
  • Nelsen, R.B., An Introduction to Copulas, 2nd edition. Springer-Verlag, New York (2006).
  • Nelsen, R.B., An Introduction to Copulas, Springer-Verlag, New York (1999).
  • Parzen, E., ”On estimation of a probability density function and mode”, Ann. Math. Statist.33, (1962) , pp.1065-1076.
  • Pickands, III, J., ”Statistical inference using extreme order statistics”, Ann. Statist.3,(1975), pp.119-131.
  • R¨uschendorf, L.,” Asymptotic distributions of multivariate rank order statistics”, Ann. Statist. 4, 5 (1976), pp.912-923.
  • Sancetta,A., ”Nonparametric estimation of multivariate distributions with given marginals: L2theory”,Cambridge Working papers in Economics No.0320, (2003).
  • Sancetta, A., Satchell,S., ”The Barnestien coplua and its application to modelling and ap- proximation of multivariate distributions”, Econometric theory, 20, (2004), pp.535-562.
  • Scott, D. W., Multivariate density estimation. Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics, John Wiley & Sons Inc., New York, (1992). Theory, practice, and visualization, A Wiley-Interscience Publication.
  • Shorack, G. R., AND Wellner, J. A., Empirical processes with applications tostatistics. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. John Wiley & Sons Inc., New York, (1986).
  • Sklar, M., ”Fonctions de r´epartition `a n dimensions et leurs marges”, Publ. Inst. Statist. Univ. Paris 8, (1959), pp.229-231.
  • Van Der Vaart, A. W., AND Wellner, J. A., Weak convergence and empirical processes, Springer Series in Statistics. Springer-Verlag, New York, (1996). With applications to statis- tics.
  • Stochastic Models, Statistics and Applications Moulay Tahar University, Saida P.O.Box.
  • 138 En-Nasr Saida 20 000 Algeria.
  • E-mail address: dbennafla@yahoo.fr
  • Department of Mathematics, Djillali Liabes University, Sidi Bel Abbes, P.O.Box. 89, Sidi Bel Abbes 22000, Algeria. E-mail address: rabhi abbes@yahoo.fr
  • E-mail address: bouchentouf amina@yahoo.fr