جلد 19، شماره 1 - ( 3-1399 )                   جلد 19 شماره 1 صفحات 163-183 | برگشت به فهرست نسخه ها


XML English Abstract Print


Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:

Susam S O. Parameter Estimation of Some Archimedean Copulas Based on Minimum Cramér-von-Mises Distance. JIRSS. 2020; 19 (1) :163-183
URL: http://jirss.irstat.ir/article-1-568-fa.html
susam selim orhun. Parameter Estimation of Some Archimedean Copulas Based on Minimum Cramér-von-Mises Distance. پژوهشنامه انجمن آمار ایران. 1399; 19 (1) :163-183

URL: http://jirss.irstat.ir/article-1-568-fa.html


Munzur University ، orhunsusam@munzur.edu.tr
چکیده:   (504 مشاهده)
The purpose of this paper is to introduce a new estimation method for estimating the Archimedean copula dependence parameter in the non-parametric setting. The estimation of the dependence parameter has been selected as the value that minimizes the Cramér-von-Mises distance which measures the distance between Empirical Bernstein Kendall distribution function and true Kendall distribution function. A Monte Carlo study is performed to measure the performance of the new estimator and compared to conventional estimation methods. In terms of estimation performance, simulation results show that the proposed Minumum Cramér-von-Mises estimation method has a good performance for low dependence and small sample size when compared
with the other estimation methods. The new minimum distance estimation of the dependence parameter is applied to model the dependence of two real data sets as illustrations.
     
نوع مطالعه: Original Paper | موضوع مقاله: 62Gxx: Nonparametric inference
دریافت: 1397/11/11 | پذیرش: 1398/6/4 | انتشار: 1399/4/14

فهرست منابع
1. Biau, G. and Wegkamp, M. (2005), Minimum distance estimation of copula densities. Statistics & Probability letters, 73, 105-114. [DOI:10.1016/j.spl.2005.02.006]
2. Deheuvels, P. (1978). Caracterisation complete des lois extremes multivariees et de la convergence des types extremes. Publications de l'Institut de Statistique de l'Universite' de Paris 3, 1-36.
3. Duchesne, T., Rioux, J. and Luong, A. (1997). Minimum crame'r-von mises distance methods for complete and grouped data. Communications in statistics - theory and methods 26, 401-420. [DOI:10.1080/03610929708831923]
4. Fermanian, J.D., Radulovic, D. and Wegkamp, M. (2004). Weak convergence of empirical copulaprocesses. Bernoulli 10, 847-860. [DOI:10.3150/bj/1099579158]
5. Genest, C. and Mackay, R.J. (1986). Copules archimediennes et families de lois bidimensionelles dont les marges sont donnees. Canadian journal of statistics 14, 145-159. [DOI:10.2307/3314660]
6. Genest, C. and Rivest, L. (1993). Statistical inference procedures for bivariate archimedean copulas. Journal of the American Statistical Association 88, 1034-1043. [DOI:10.1080/01621459.1993.10476372]
7. Genest, C., Molina, J. and Lallena, J. (1995), De l'impossibilite de construire des lois a marges multidimensionnelles donnees a partir de copules. Comptes rendus de l'Acadmie des Sciences, 320, 723-726.
8. Genest, C., Rémillard, B. and Beaudoin, D. (2008), Goodness-of-fit tests for copulas: A review and a power study. Insurance: Mathematics and Economics, 44, 199-213. [DOI:10.1016/j.insmatheco.2007.10.005]
9. Joe, H. (1978). Asymptotic efficiency of the two-stage estimation method for copula-based models. Journal of Multivariate Analysis 94, 401-419. [DOI:10.1016/j.jmva.2004.06.003]
10. Joe, H. and Xu, J. (1996). The estimation method of inference functions for margins for multivariate models.Technical Report 166, UBC, Department of Statistics.
11. Joe, H. (1997). Multivariate Models and Dependence Concepts. London, England: Chapman and Hall. [DOI:10.1201/b13150]
12. Joe, H. (2005), Asymptotic e ciency of the two-stage estimation method for copula-based models. Journal of Multivariate Analysis, 94, 401-419. [DOI:10.1016/j.jmva.2004.06.003]
13. Kim, G., Silvapulle, M. and Silvapul, P. (2007). Comparison of semiparametric and parametric methods for estimating copulas. Communications in Statistics. Simulation and Computation 51, 2836-2850. [DOI:10.1016/j.csda.2006.10.009]
14. Kojadinovic, I. and Yan, J. (2010). Comparison of three semiparametric methods for estimating dependence parameters in copula models. Insurance: Mathematics and Economics 47, 52-63. [DOI:10.1016/j.insmatheco.2010.03.008]
15. Leblanc, A. (2012). On estimating distribution functions using bernstein polynomials. Annals of the Institute of Statistical Mathematics 64, 919-943. [DOI:10.1007/s10463-011-0339-4]
16. Mendes, B., De Melo B. and Nelsen, R. (2007), Robust fits for copula models. Communications in statistics: Simulation and computition, 36(5), 997-1017. [DOI:10.1080/03610910701539708]
17. Michiels, F., Koch, I. and De Schepper, A. (2012), How to improve the fit of Archimedean copulas by means of transforms. Statistical Papers, 53, 345-355. [DOI:10.1007/s00362-010-0341-6]
18. Najafabadi, A., Farid-Rohani, M. and Qazvini, M. (2013), A GLM-Based Method to Estimate a Copula's Parameter(s). Journal of the Iranian statistical society, 12(2), 321-334.
19. Nelsen, R.B. (2006). An introduction to copulas. New York, USA: Springer.
20. Oakes, D. (1994). Multivariate survival distributions. Journal of Nonparameric Statistics 3, 343-354. [DOI:10.1080/10485259408832593]
21. Sklar, A. (1959). Fonctions de re'partition a' n dimensions et leurs marges. Publications de l'Institut de Statistique de l'Universite' de Paris 8, 229-231.
22. Susam, S.O. and Ucer, B.U. (2018). Testing independence for archimedean copula based on bernstein estimate of kendall distribution function. Journal of Statistical Computation and Simulation 88, 2589-2599. [DOI:10.1080/00949655.2018.1478978]
23. Tsukahara H. (2005), Semiparametric estimation in copula models. Canadian Journal of Statistics, 33(3), 357-375. [DOI:10.1002/cjs.5540330304]
24. Weib, G. (2011). Copula parameter estimation by maximum-likelihood and minimum-distance estimators: a simulation study. Computitional Statistics 26, 31-54. [DOI:10.1007/s00180-010-0203-7]

ارسال پیام به نویسنده مسئول


کلیه حقوق این وب سایت متعلق به پژوهشنامه انجمن آمار ایران می باشد.

طراحی و برنامه نویسی : یکتاوب افزار شرق

© 2020 All Rights Reserved | Journal of The Iranian Statistical Society

Designed & Developed by : Yektaweb