Research Article
BibTex RIS Cite

Comparison of Some Selection Criteria for Selecting Bivariate Archimedean Copulas

Year 2016, Volume: 16 Issue: 2, 250 - 255, 30.04.2016

Abstract

Commonly, while selecting an appropriate bivariate Archimedean copula function that models
data, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and minimum
distance (MD) are used as a selection criterion. In this study, the performances of these
criteria for selecting copula function are investigated by some simulation studies.

References

  • Atkinson, A., 1969. A test for discriminating between models. Biometrika 56, 337‐341
  • Atkinson, A., 1970. A method for discriminating between models. Journal of the Royal statistical Society, Series B32, 323‐353.
  • Belgorodski, N., 2010. Selecting pair copula families for regular vines with application to the multivariate analysis of European stock market indices. Master Thesis, Technische Universität München.
  • Clayton, D.G., 1978. A Model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika, 65, 141–151.
  • Cox, D.R., 1962. Further Results on tests of seperate families of hypotheses. Journal of the Royal Statistical Society, Series B24, 406‐424.
  • durrleman, V., Nikeghbali, A., and Roncalli, T., 2000. Which copula is the right one? Technical Report Groupe de Researche operationnelle Credit‐ Lyonnois.
  • Frank, M.J., 1979. On the simultaneous associativity of F(x,y) and x+y‐F(x,y). Aequationes Mathematicae, 19, 194–226.
  • Frees, W.E. and Valdez, A.E., 1997. Understanding relationships using copulas. 32nd. Actuarial Research Conference, 6‐8 August at University of Calgary, Albert ,Canada.
  • Genest, C., and Rivest, L.P., 1993. Statistical inference procedures for bivariate archimedean copulas. Journal of the American Statistical Association Theory and Methods ,88, No: 423
  • Genest, C., Rémillard, B. and Beaudoin, D., 2009. goodness‐of‐fit tests for copulas: A review and apower study. Insurance: Mathematics and Economics, 44,199‐213.
  • Grønneberg, S., and Hjort N.L., 2014. The Copula Information Criteria. Scandinavian Journal of Statistics, 41,436‐459.
  • Gumbel, E.J., 1960. Bivariate exponential distributions. Journal of the American Statistical Association, 55, 698–707.
  • Huard, D.,Evin, G., and Favre, A.C., 2006. Bayesian copula selection. Computational Statistics&Data Analysis, 51(2), 809‐822.
  • Joe, H., 1997. Multivariate Models and Dependence Concepts. Chapman & Hall Ltd. Nelsen, R., 2006. An Introduction to Copulas. Springer, NewYork.
  • R‐Development Core Team (2012). R: A Language and Environment for Statistical Computing (computer software). Available from: http://www.R‐project.org.
  • Sklar, A., 1959. Fonctions de repartition a n dimensions et leurs marges., Publications del'Institut de Statistique de l’Universite de Paris,8, 229‐231.Sklar, A., 1973. Random variables, joint distribution functions and copulas. Kybernetika, 9,449–460.
  • Schweizer, B., and Sklar, A. 1983. Probabilistic Metric Spaces. North‐Holland, New York.
  • Wolfowitz, J., 1957. The minimum distance method. Ann. Math. Statist., 28, 75‐87.
Year 2016, Volume: 16 Issue: 2, 250 - 255, 30.04.2016

Abstract

References

  • Atkinson, A., 1969. A test for discriminating between models. Biometrika 56, 337‐341
  • Atkinson, A., 1970. A method for discriminating between models. Journal of the Royal statistical Society, Series B32, 323‐353.
  • Belgorodski, N., 2010. Selecting pair copula families for regular vines with application to the multivariate analysis of European stock market indices. Master Thesis, Technische Universität München.
  • Clayton, D.G., 1978. A Model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika, 65, 141–151.
  • Cox, D.R., 1962. Further Results on tests of seperate families of hypotheses. Journal of the Royal Statistical Society, Series B24, 406‐424.
  • durrleman, V., Nikeghbali, A., and Roncalli, T., 2000. Which copula is the right one? Technical Report Groupe de Researche operationnelle Credit‐ Lyonnois.
  • Frank, M.J., 1979. On the simultaneous associativity of F(x,y) and x+y‐F(x,y). Aequationes Mathematicae, 19, 194–226.
  • Frees, W.E. and Valdez, A.E., 1997. Understanding relationships using copulas. 32nd. Actuarial Research Conference, 6‐8 August at University of Calgary, Albert ,Canada.
  • Genest, C., and Rivest, L.P., 1993. Statistical inference procedures for bivariate archimedean copulas. Journal of the American Statistical Association Theory and Methods ,88, No: 423
  • Genest, C., Rémillard, B. and Beaudoin, D., 2009. goodness‐of‐fit tests for copulas: A review and apower study. Insurance: Mathematics and Economics, 44,199‐213.
  • Grønneberg, S., and Hjort N.L., 2014. The Copula Information Criteria. Scandinavian Journal of Statistics, 41,436‐459.
  • Gumbel, E.J., 1960. Bivariate exponential distributions. Journal of the American Statistical Association, 55, 698–707.
  • Huard, D.,Evin, G., and Favre, A.C., 2006. Bayesian copula selection. Computational Statistics&Data Analysis, 51(2), 809‐822.
  • Joe, H., 1997. Multivariate Models and Dependence Concepts. Chapman & Hall Ltd. Nelsen, R., 2006. An Introduction to Copulas. Springer, NewYork.
  • R‐Development Core Team (2012). R: A Language and Environment for Statistical Computing (computer software). Available from: http://www.R‐project.org.
  • Sklar, A., 1959. Fonctions de repartition a n dimensions et leurs marges., Publications del'Institut de Statistique de l’Universite de Paris,8, 229‐231.Sklar, A., 1973. Random variables, joint distribution functions and copulas. Kybernetika, 9,449–460.
  • Schweizer, B., and Sklar, A. 1983. Probabilistic Metric Spaces. North‐Holland, New York.
  • Wolfowitz, J., 1957. The minimum distance method. Ann. Math. Statist., 28, 75‐87.
There are 18 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Çiğdem Topçu Gülöksüz This is me

Publication Date April 30, 2016
Submission Date May 4, 2016
Published in Issue Year 2016 Volume: 16 Issue: 2

Cite

APA Topçu Gülöksüz, Ç. (2016). Comparison of Some Selection Criteria for Selecting Bivariate Archimedean Copulas. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 16(2), 250-255.
AMA Topçu Gülöksüz Ç. Comparison of Some Selection Criteria for Selecting Bivariate Archimedean Copulas. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. April 2016;16(2):250-255.
Chicago Topçu Gülöksüz, Çiğdem. “Comparison of Some Selection Criteria for Selecting Bivariate Archimedean Copulas”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 16, no. 2 (April 2016): 250-55.
EndNote Topçu Gülöksüz Ç (April 1, 2016) Comparison of Some Selection Criteria for Selecting Bivariate Archimedean Copulas. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 16 2 250–255.
IEEE Ç. Topçu Gülöksüz, “Comparison of Some Selection Criteria for Selecting Bivariate Archimedean Copulas”, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 16, no. 2, pp. 250–255, 2016.
ISNAD Topçu Gülöksüz, Çiğdem. “Comparison of Some Selection Criteria for Selecting Bivariate Archimedean Copulas”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 16/2 (April 2016), 250-255.
JAMA Topçu Gülöksüz Ç. Comparison of Some Selection Criteria for Selecting Bivariate Archimedean Copulas. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2016;16:250–255.
MLA Topçu Gülöksüz, Çiğdem. “Comparison of Some Selection Criteria for Selecting Bivariate Archimedean Copulas”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 16, no. 2, 2016, pp. 250-5.
Vancouver Topçu Gülöksüz Ç. Comparison of Some Selection Criteria for Selecting Bivariate Archimedean Copulas. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2016;16(2):250-5.