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Asymptotics for Kotz Type III elliptical distributions

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  • Hashorva, Enkelejd

Abstract

Let be a Kotz Type III elliptical random vector in , and let tn,n>=1 be positive constants such that limn-->[infinity]tn=[infinity]. In this article we obtain an asymptotic expansion of . As an application we derive an approximation for the conditional excess distribution and show the asymptotic dependence of Kotz Type III triangular arrays. Further, we provide some details on the estimation of conditional excess distributions and survivor function of Kotz Type III random vectors.

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  • Hashorva, Enkelejd, 2009. "Asymptotics for Kotz Type III elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 927-935, April.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:7:p:927-935
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    References listed on IDEAS

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    1. Schmidt, Rafael & Schmieder, Christian, 2009. "Modelling dynamic portfolio risk using risk drivers of elliptical processes," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 229-244, April.
    2. Hashorva, Enkelejd, 2006. "On the multivariate Hüsler-Reiss distribution attracting the maxima of elliptical triangular arrays," Statistics & Probability Letters, Elsevier, vol. 76(18), pages 2027-2035, December.
    3. Enkelejd Hashorva & Jürg Hüsler, 2003. "On multivariate Gaussian tails," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(3), pages 507-522, September.
    4. Berman, Simeon M., 1983. "Sojourns and extremes of Fourier sums and series with random coefficients," Stochastic Processes and their Applications, Elsevier, vol. 15(3), pages 213-238, August.
    5. Hüsler, Jürg & Reiss, Rolf-Dieter, 1989. "Maxima of normal random vectors: Between independence and complete dependence," Statistics & Probability Letters, Elsevier, vol. 7(4), pages 283-286, February.
    6. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    7. Friedrich Schmid & Rafael Schmidt, 2007. "Nonparametric inference on multivariate versions of Blomqvist’s beta and related measures of tail dependence," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 66(3), pages 323-354, November.
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    Cited by:

    1. Nadarajah, Saralees, 2015. "Complete asymptotic expansions for normal extremes," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 127-133.

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