On the residual dependence index of elliptical distributions

Statistics and Probability Letters

Volumn 80, Issue 13-14, 2010, Pages 1070-1078

  Hashorva, Enkelejd ^a  

^a UNIVERSITY OF BERN   (Switzerland)

Author keywords

Elliptical distribution; Gumbel max domain of attraction; Partial residual dependence index; Quadratic programming problem; Weibull tail distribution

Indexed keywords

EID: 77953026441     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spl.2010.03.001     Document Type: Article

References (45)

1. Abdous B., Fougères A.-L., Ghoudi K. Extreme behaviour for bivariate elliptical distributions. Canad. J. Statist. 2005, 33(3):317-334.
2. Abdous B., Fougères A.-L., Ghoudi K., Soulier P. Estimation of bivariate excess probabilities for elliptical models. Bernoulli 2008, 14(4):1065-1088.
3. Berman M.S. Sojourns and extremes of stationary processes. Ann. Probab. 1982, 10:1-46.
4. Berman M.S. Sojourns and extremes of Fourier sums and series with random coefficients. Stochastic Process. Appl. 1983, 15:213-238.
5. Berman M.S. Sojourns and Extremes of Stochastic Processes 1992, Wadsworth & Brooks/Cole, Boston.
6. Cambanis S., Huang S., Simons G. On the theory of elliptically contoured distributions. J. Multivariate Anal. 1981, 11(3):368-385.
7. Dai M., Mukherjea A. Identification of the parameters of a multivariate normal vector by the distribution of the minimum. J. Theoret. Probab. 2001, 14(1):267-298.
8. de Haan L., Ferreira A. Extreme Value Theory. An Introduction 2006, Springer, New York.
9. De Haan L., Peng L. Comparison of tail index estimators. Statist. Neerlandica 1998, 52(1):60-70.
10. Diebolt J., Gardes L., Girard S., Guillou A. Bias-reduced extreme quantiles estimators of Weibull distributions. J. Statist. Plann. Inference 2008, 138(5):1389-1401.
11. Eddy W.F., Gale J.D. The convex hull of a spherically symmetric sample. Adv. Appl. Probab. 1981, 13:751-763.
12. Embrechts P., Klüppelberg C., Mikosch T. Modelling Extremal Events for Insurance and Finance 1997, Springer, Berlin.
13. Falk M., Hüsler J., Reiss R.-D. Laws of Small Numbers: Extremes and Rare Events. DMV Seminar 2004, vol. 23. Birkhäuser, Basel. second ed.
14. Fang K.-T., Kotz S., Ng K.-W. Symmetric Multivariate and Related Distributions 1990, Chapman and Hall, London, United Kingdom.
15. Gale, J.D., 1980. The asymptotic distribution of the convex hull of a random sample, Ph.D. Thesis, Carnegie-Mellon University.
16. Gardes L., Girard S. Comparison of Weibull tail-coefficient estimators. REVSTAT 2006, 4(2):163-188.
17. Girard S. A Hill type estimator of the Weibull tail-coefficient. Comm. Statist. Theory Methods 2004, 33(2):205-234.
18. Hashorva E. Extremes of asymptotically spherical and elliptical random vectors. Insurance Math. Econom. 2005, 36(3):285-302.
19. Hashorva E. Asymptotics and bounds for multivariate Gaussian tails. J. Theoret. Probab. 2005, 18(1):79-97.
20. Hashorva E. Gaussian approximation of conditional elliptical random vectors. Stoch. Models 2006, 22(3):441-457.
21. Hashorva E. On the regular variation of elliptical random vectors. Statist. Probab. Lett. 2006, 76(14):1427-1434.
22. Hashorva E. Exact tail asymptotics for type I bivariate elliptical distributions. Albanian J. Math. 2007, 1(2):99-114.
23. Hashorva E. Asymptotics properties of type I elliptical random vectors. Extremes 2007, 10(4):175-206.
24. Hashorva E. Conditional limiting distribution of beta-independent random vectors. J. Multivariate Anal. 2008, 99(8):1438-1459.
25. Hashorva E. Conditional limit results for type I polar distributions. Extremes 2009, 12:239-263.
26. Hashorva E. Conditional limits of Wp scale mixture distributions. J. Statist. Plann. Inference 2009, 139(10):3501-3511.
27. Hashorva E., Hüsler J. Remarks on compound Poisson approximation of Gaussian random sequences. Statist. Probab. Lett. 2002, 57(1):1-8.
28. Hüsler J., Li D. Testing asymptotic independence in bivariate extremes. J. Statist. Plann. Inference 2009, 139:990-998.
29. Klüppelberg C., Kuhn K., Peng L. Estimating the tail dependence of an elliptical distribution. Bernoulli 2007, 13(1):229-251.
30. Krajina, A., 2009. A method of moments estimator of tail dependence in elliptical copula models, Center Discussion Paper, 2009-42.
31. Li D., Peng L. Goodness-of-fit test for tail copulas modeled by elliptical copulas. Statist. Probab. Lett. 2009, 79(8):1097-1104.
32. Liu, Y., Tang, Q., 2010. Subexponentiality of the product convolution of two Weibull-type distributions, J. Aust. Math. Soc. (in press).
33. Peng L. Second Order Condition and Extreme Value Theory. Tinbergen Institute Research Series 1998, vol. 178. Thesis Publisher, Amsterdam.
34. Peng L. Estimating the probability of a rare event via elliptical copulas. N. Am. Actuar. J. 2008, 12(2):116-128.
35. Peng L. A practical way for estimating tail dependence functions. Statist. Sinica 2010, 20:365-378.
36. Manner, H., Segers, J., 2009. Tails of correlation mixtures of elliptical copulas. arxiv:0912.3516.
37. Reiss R.-D. Approximate Distributions of Order Statistics: With Applications to Nonparametric Statistics 1989, Springer, New York.
38. Reiss R.-D., Thomas M. Statistical Analysis of Extreme Values. From Insurance, Finance, Hydrology and Other Fields 2007, Birkhäuser, Basel. third ed.
39. Resnick S.I. Extreme Values, Regular Variation and Point Processes 1987, Springer, New York.
40. Resnick S.I. Hidden regular variation, second order regular variation and asymptotic independence. Extremes 2002, 5(4):303-336.
41. Sarr, A., Gupta, A.K., 2009. Estimation of the precision matrix of multivariate Kotz type model, J. Multivariate Anal., Available online.
42. Tang Q. The subexponentiality of products revisited. Extremes 2006, 9(3-4):231-241.
43. Tang Q. From light tails to heavy tails through multiplier. Extremes 2008, 11(4):379-391.
44. Tang Q., Tsitsiashvili G. Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks. Stochastic Process. Appl. 2003, 108(2):299-325.
45. Tang Q., Tsitsiashvili G. Finite- and infinite-time ruin probabilities in the presence of stochastic returns on investments. Adv. Appl. Probab. 2004, 36(4):1278-1299.