Convergence of Archimedean copulas. (English) Zbl 1139.62303
Summary: Convergence of a sequence of bivariate Archimedean copulas to another Archimedean copula or to the comonotone copula is shown to be equivalent with convergence of the corresponding sequence of Kendall’s distribution functions. No extra differentiability conditions on the generators are needed.
MSC:
| 62E20 | Asymptotic distribution theory in statistics |
| 62H20 | Measures of association (correlation, canonical correlation, etc.) |
References:
| [1] | Barbe, Ph.; Genest, C.; Ghoudi, K.; Rémillard, B., On Kendall’s process, J. Multivariate Anal., 58, 197-229 (1996) · Zbl 0862.60020 |
| [2] | Charpentier, A., Segers, J., 2006. Lower tail dependence for Archimedean copulas: characterizations and pitfalls. Insurance Math. Econom. 40, 525-532.; Charpentier, A., Segers, J., 2006. Lower tail dependence for Archimedean copulas: characterizations and pitfalls. Insurance Math. Econom. 40, 525-532. · Zbl 1183.62086 |
| [3] | Genest, C.; MacKay, R. J., Copules archimédiennes et familles de lois bidimensionnelles dont les marges sont données, La rev. canad. statist., 14, 145-159 (1986) · Zbl 0605.62049 |
| [4] | Genest, C.; Rivest, L. P., Statistical inference procedures for bivariate Archimedean copulas, J. Amer. Statist. Assoc., 88, 1034-1043 (1993) · Zbl 0785.62032 |
| [5] | Genest, C.; Quessy, J.-F.; Rémillard, B., Goodness-of-fit procedures for copula models based on the probability integral transformation, Scand. J. Statist., 33, 337-366 (2006) · Zbl 1124.62028 |
| [6] | Juri, A.; Wüthrich, M. V., Copula convergence theorems for tail events, Insurance Math. Econom., 30, 411-427 (2002) · Zbl 1039.62043 |
| [7] | Kimberling, C. H., A probabilistic interpretation of complete monotonicity, Aequationes Math., 10, 152-164 (1974) · Zbl 0309.60012 |
| [8] | Marshall, A. W.; Olkin, I., Families of multivariate distributions, J. Amer. Statist. Assoc., 83, 834-841 (1988) · Zbl 0683.62029 |
| [9] | Nelsen, R. B., An Introduction to Copulas. Lecture Notes in Statistics, vol. 139 (1999), Springer: Springer New York · Zbl 0909.62052 |
| [10] | Oakes, D., Bivariate survival models induced by frailties, J. Amer. Statist. Assoc., 84, 487-493 (1989) · Zbl 0677.62094 |
| [11] | Prange, D., Scherer, S., 2006. Correlation smile matching with \(\operatorname{Α;} \)-stable distributions and fitted Archimedean copula models. Available online at \(\langle;\) http://www.defaultrisk.com \(\rangle;\).; Prange, D., Scherer, S., 2006. Correlation smile matching with \(\operatorname{Α;} \)-stable distributions and fitted Archimedean copula models. Available online at \(\langle;\) http://www.defaultrisk.com \(\rangle;\). · Zbl 1182.91077 |
| [12] | Schweizer, B.; Sklar, A., Probabilistic Metric Spaces (1983), North-Holland: North-Holland New York · Zbl 0546.60010 |
| [13] | Wang, W.; Wells, M. T., Model selection and semiparametric inference for bivariate failure-time data, J. Amer. Statist. Assoc., 95, 62-72 (2000) · Zbl 0996.62091 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
