A primer on copulas for count data

ASTIN Bulletin

Volumn 37, Issue 2, 2007, Pages 475-515

  Genest, Christian ^a   Nešlehová, Johanna ^b  

^a UNIVERSITÉ LAVAL   (Canada)

^b ETH ZURICH   (Switzerland)

Author keywords

Bernoulli distribution; Copulas; Count data; Discrete distribution; Geometric distribution; Kendall's tau; Poisson distribution; Spearman's p; Subcopula

Indexed keywords

EID: 37349025545     PISSN: 05150361     EISSN: 17831350     Source Type: Journal    
DOI: 10.2143/AST.37.2.2024077     Document Type: Review

References (47)

1. AVÉROUS, J. and DORTET-BERNADET, J.-L. (2000) LTD and RTI dependence orderings. Canad. J Statist., 28, 151-157.
2. CAMERON, A.C., LI, T., TRIVEDI, P.K. and ZIMMER, D.M. (2004) Modeling the differences in counted outcomes using bivariate copula models: With application to mismeasured counts. Econom. J., 7, 566-584.
3. CAPÉRAÀ, P. and GENEST, C. (1990) Concepts de dépendance et ordres stochastiques pour des lois bidimensionnelles. Canad. J. Statist., 18, 315-326.
4. CARLEY, H. (2002) Maximum and minimum extensions of finite subcopulas. Comm. Statist. Theory Methods, 31, 2151-2166.
5. CHOULAKIAN, V. and DE TIBEIRO, J. (2000) Copules archimédiennes et tableaux de contingence à variables qualitatives ordinales. Rev. Statist. Appl., 48, 83-96.
6. CONTI, P.L. (1993) On some descriptive aspects of measures of monotone dependence. Metron, 51, 43-60 (1994).
7. DENUIT, M. and LAMBERT, P. (2005) Constraints on concordance measures in bivariate discrete data. J. Multivariate Anal., 93, 40-57.
8. EMBRECHTS, P., MCNEIL, A.J. and STRAUMANN, D. (2002) Correlation and dependence in risk management: Properties and pitfalls. In Risk Management: Value at Risk and Beyond (Cambridge, 1998), pages 176-223. Cambridge Univ. Press, Cambridge.
9. ESARY, J.D. and PROSCHAN, F. (1972) Relationships among some concepts of bivariate dependence. Ann. Math. Statist., 43, 651-655.
10. FANG, Z. and JOE, H. (1992) Further developments on some dependence orderings for continuous bivariate distributions. Ann. Inst. Statist. Math., 44, 501-517.
11. FREES, E.W. and VALDEZ, E.A. (1998) Understanding relationships using copulas. N. Amer. Act. J., 2, 1-25.
12. GENEST, C. and FAVRE, A.-C. (2007) Everything you always wanted to know about copula modeling but were afraid to ask. J. Hydrologic Eng., 12, 347-368.
13. GENEST, C., GHOUDI, K. and RIVEST, L.-P. (1995) A semiparametric estimation procedure of dependence parameters in multivariate families of distributions. Biometrika, 82, 543-552.
14. GENEST, C., MARCEAU, É. and MESFIOUI, M. (2003) Compound Poisson approximations for individual models with dependent risks. Insurance Math. Econom., 32, 73-91.
15. GENEST, C. and RÉMILLARD, B. (2004) Tests of independence and randomness based on the empirical copula process. Test, 13, 335-370.
16. GENEST, C., RÉMILLARD, B. and BEAUDOIN, D. (2007) Omnibus goodness-of-fit tests for copulas: A review and a power study. Insurance Math. Econom., 42, in press.
17. GOODMAN, L.A. and KRUSKAL, W.H. (1954) Measures of association for cross classifications. J. Amer. Statist. Assoc., 49, 732-764.
18. HOEFFDING, W. (1940) Maβstabinvariante Korrelationstheorie für diskontinuierliche Verteilungen. Arch. Math. Wirt. Sozialforsch., 7, 4-70.
19. JOE, H. (1993) Multivariate dependence measures and data analysis. Comput. Statist. Data Anal., 16, 279-297.
20. JOE, H. (1997) Multivariate Models and Dependence Concepts, volume 73 of Monographs on Statistics and Applied Probability. Chapman & Hall, London.
21. JOE, H. (2005) Asymptotic efficiency of the two-stage estimation method for copula-based models. J. Multivariate Anal., 94, 401-419.
22. KENDALL, M.G. (1945) The treatment of ties in ranking problems. Biometrika, 33, 239-251.
23. KIM, G., SILVAPULLE, M.J. and SILVAPULLE, P. (2007) Comparison of serniparametric and parametric methods for estimating copulas. Comput. Statist. Data Anal., 51, 2836-2850.
24. KIMELDORF, G. and SAMPSON, A.R. (1987) Positive dependence orderings. Ann. Inst. Statist. Math., 39, 113-128.
25. KOWALCZYK, T. and NIEWIADOMSKA-BUGAJ, M. (2001) An algorithm for maximizing Kendall's τ. Comput. Statist. Data Anal., 37, 181-193.
26. LEHMANN, E.L. (1966) Some concepts of dependence. Ann. Math. Statist., 37, 1137-1153.
27. MARSHALL, A.W. (1996) Copulas, marginals, and joint distributions. In Distributions with Fixed Marginals and Related Topics (Seattle, WA, 1993), volume 28 of IMS Lecture Notes Monogr. Ser., pages 213-222. Inst. Math. Statist., Hayward, CA.
28. MCNEIL, A.J., FREY, R. and EMBRECHTS, P. (2005) Quantitative Risk Management: Concepts, Techniques, and Tools. Princeton University Press, Princeton, NJ.
29. MEESTER, S.G. and MACKAY, R.J. (1994) A parametric model for cluster correlated categorical data. Biometrics, 50, 954-963.
30. MESFIOUI, M. and TAJAR, A. (2005) On the properties of some nonparametric; concordance measures in the discrete case. J. Nonparametr. Stat., 17, 541-554.
31. MIKUSIŃSKI, P., SHERWOOD, H. and TAYLOR, M.D. (1992) Shuffles of min. Stochastica, 13, 61-74.
32. NELSEN, R.B. (1987) Discrete bivariate distributions with given marginals and correlation. Comm. Statist. B-Simulation Comput., 16, 199-208.
33. NELSEN, R.B. (1999) An Introduction to Copulas, volume 139 of Lecture Notes in Statistics. Springer, New York.
34. NEŠLEHOVÁ, J. (2004) Dependence of Non-Continuous Random Variables. Doctoral dissertation, Universität Oldenburg, Oldenburg, Germany.
35. NEŠLEHOVÁ, J. (2007) On rank correlation measures for non-continuous random variables. J. Multivariate Anal., 98, 544-567.
36. OAKES, D. (1982) A model for association in bivariate survival data. J. Roy. Statist. Soc. Ser. B, 44, 414-422.
37. PFEIFER, D. and NEŠEHOVÁ, J. (2004) Modeling and generating dependent risk processes for IRM and DFA. Astin Bull., 34, 333-360.
38. SCARSINI, M. (1984) On measures of concordance. Stochastica, 8, 201-218.
39. SCHWEIZER, B. and SKLAR, A. (1974) Operations on distribution functions not derivable from operations on random variables. Studia Math., 52, 43-52.
40. SHIN, J.H. and LOUIS, T.A. (1995) Inferences on the association parameter in copula models for bivariate survival data. Biometrics, 51, 1384-1399.
41. SKLAR, A. (1959) Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris, 8, 229-231.
42. TCHEN, A.H. (1980) Inequalities for distributions with given marginals. Ann. Probab., 8, 814-827.
43. TRÉGOUËT, D.-A., DUCIMETIÈRE, P., BOCQUET, V., VISVIKIS, S., SOUBRIER, F. and TIRET, L. (2004) A parametric copula model for analysis of familial binary data. Am. J. Hum. Genet., 64, 886-893.
44. VANDENHENDE, F. and LAMBERT, P. (2003) Improved rank-based dependence measures for categorical data. Statist. Probab. Lett., 63, 157-163.
45. WHITT, W. (1976) Bivariate distributions with given marginals. Ann. Statist., 4, 1280-1289.
46. YAARI, M.E. (1987) The dual theory of choice under risk. Econometrica, 55, 95-115.
47. YANAGIMOTO, T. and OKAMOTO, M. (1969) Partial orderings of permutations and monotonicity of a rank correlation statistic. Ann. Inst. Statist. Math., 21, 489-506.