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On the extremal dependence coefficient of multivariate distributions. (English) Zbl 1120.62035
Summary: A measure called ‘extremal dependence coefficient’ (EDC) is introduced for studying the asymptotic dependence structure of the minimum and the maximum of a random vector. Some general properties of the EDC are derived and its relation to the tail dependence coefficient is examined. The extremal dependence structure of regularly varying elliptical random vectors is investigated and it is shown that the EDC is only determined by the tail index and by the pseudo-correlation coefficients of the elliptical distribution.

MSC:
62H05 Characterization and structure theory for multivariate probability distributions; copulas
62H20 Measures of association (correlation, canonical correlation, etc.)
62E20 Asymptotic distribution theory in statistics
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[1] Abdous, B.; Genest, C.; Rémillard, B., Dependence properties of meta-elliptical distributions, (), 1-15
[2] Basrak, B.; Davis, R.A.; Mikosch, T., A characterization of multivariate regular variation, Ann. appl. probab., 12, 908-920, (2002) · Zbl 1070.60011
[3] Bilodeau, M.; Brenner, D., Theory of multivariate statistics, (1999), Springer Berlin · Zbl 0930.62054
[4] Cambanis, S.; Huang, S.; Simons, G., On the theory of elliptically contoured distributions, J. multivariate anal., 11, 368-385, (1981) · Zbl 0469.60019
[5] Demarta, S.; McNeil, A.J., The t copula and related copulas, Internat. statist. rev., 73, 111-129, (2005) · Zbl 1104.62060
[6] Embrechts, P.; Klüppelberg, C.; Mikosch, T., Modelling extremal events for insurance and finance, (1997), Springer Berlin · Zbl 0873.62116
[7] Fang, K.T.; Kotz, S.; Ng, K.W., Symmetric multivariate and related distributions, (1990), Chapman & Hall New York
[8] Frahm, G.; Junker, M.; Szimayer, A., Elliptical copulas: applicability and limitations, Statist. probab. lett., 63, 275-286, (2003) · Zbl 1116.62352
[9] Hult, H.; Lindskog, F., Multivariate extremes, aggregation and dependence in elliptical distributions, Adv. appl. probab., 34, 587-608, (2002) · Zbl 1023.60021
[10] Joe, H., Multivariate models and dependence concepts, (1997), Chapman & Hall New York · Zbl 0990.62517
[11] Mikosch, T., Modeling dependence and tails of financial time series, (), 185-286
[12] Nelsen, R.B., Dependence and order in families of Archimedean copulas, J. multivariate anal., 60, 111-122, (1997) · Zbl 0883.62049
[13] Nelsen, R.B., An introduction to copulas, (1999), Springer Berlin · Zbl 0909.62052
[14] Schmidt, R., Tail dependence for elliptically contoured distributions, Math. methods oper. res., 55, 301-327, (2002) · Zbl 1015.62052
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