Second-order refined peaks-over-threshold modelling for heavy-tailed distributions

Journal of Statistical Planning and Inference

Volumn 139, Issue 8, 2009, Pages 2800-2815

  Beirlant, Jan ^a   Joossens, Elisabeth ^b   Segers, Johan ^c  

^a Katholieke Universiteit Leuven   (Belgium)

^b JOINT RESEARCH CENTRE   (Italy)

^c UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

Bias reduction; Extended Pareto distribution; Extreme value index; Heavy tails; Hill estimator; Regular variation; Tail empirical process; Tail probability; Weissman probability estimator

Indexed keywords

EID: 67349251218     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2009.01.006     Document Type: Article

References (33)

1. Balkema A.A., and de Haan L. Residual life time at great age. Ann. Probab. 2 (1974) 792-804
2. Beirlant J., Bouquiaux C., and Werker B.J. Semiparametric lower bounds for tail index estimation. J. Statist. Plann. Inference 136 (2006) 705-729
3. Beirlant J., Dierckx G., Goegebeur Y., and Matthys G. Tail index estimation and an exponential regression model. Extremes 2 (1999) 177-200
4. Beirlant J., Dierckx G., Guillou A., and Stǎricǎ C. On exponential representations of log-spacings of extreme order statistics. Extremes 5 (2002) 157-180
5. Beirlant J., Goegebeur Y., Segers J., and Teugels J. Statistics of Extremes: Theory and Applications (2004), Wiley, Chichester
6. Beirlant, J., Joossens, E., Segers, J., 2002b. Modelling excesses over high thresholds by perturbed generalized Pareto distributions. Technical Report 2002-030, EURANDOM, Eindhoven.
7. Bingham N.H., Goldie C.M., and Teugels J.L. Regular Variation (1987), Cambridge University Press, Cambridge
8. Coles S.G. An Introduction to Statistical Modelling of Extreme Values. Springer Series in Statistics (2001), Springer, London
9. Cooray K., and Ananda M.A. Modeling actuarial data with a composite lognormal-Pareto model. Scand. Actuar. J. 5 (2005) 321-334
10. Davison A.C., and Smith R.L. Models for exceedances over high thresholds. J. Roy. Statist. Soc. Ser. B 52 (1990) 393-442
11. de Haan L., and Ferreira A. Extreme Value Theory: An Introduction (2006), Springer, New York
12. de Haan L., and Stadtmüller U. Generalized regular variation of second order. J. Austral. Math. Soc. (Ser. A) 61 (1996) 381-395
13. Drees H. Refined Pickands estimators with bias correction. Comm. Statist. Theory Methods 25 (1996) 837-851
14. Drees H. A general class of estimators of the extreme value index. J. Statist. Plann. Inference 66 (1998) 95-112
15. Drees H., Ferreira A., and de Haan L. On maximum likelihood estimation of the extreme value index. Ann. Appl. Probab. 14 (2004) 1179-1201
16. Feuerverger A., and Hall P. Estimating a tail exponent by modelling departure from a Pareto distribution. Ann. Statist. 27 (1999) 760-781
17. Fraga Alves M.I., de Haan L., and Lin T. Estimation of the parameter controlling the speed of convergence in extreme value theory. Math. Methods Statist. 12 (2003) 155-176
18. Fraga Alves M.I., Gomes M.I., and de Haan L. A new class of semi-parametric estimators of the second order parameter. Portugal. Math. 60 (2003) 193-214
19. Frigessi A., Haug O., and Rue H. A dynamic mixture model for unsupervised tail estimation without threshold selection. Extremes 5 (2002) 219-235
20. Geluk, J., de Haan, L., 1987. Regular variation, extensions and Tauberian theorems. Technical Report 40, CWI tract, Amsterdam.
21. Gomes M.I., and Martins M.J. Asymptotically unbiased estimators of the tail index based on external estimation of the second order parameter. Extremes 5 (2002) 5-31
22. Gomes M.I., and Martins M.J. Bias reduction and explicit semi-parametric estimation of the tail index. J. Statist. Plann. Inference 124 (2004) 361-378
23. Gomes M.I., Martins M.J., and Neves M. Alternatives to a semi-parametric estimator of parameters of rare events-the Jackknife methodology. Extremes 3 (2000) 207-229
24. Hall P. On some simple estimates of an exponent of regular variation. J. Roy. Statist. Soc. Ser. B 44 (1982) 37-42
25. Hill B.M. A simple approach to inference about the tail of a distribution. Ann. Statist. 3 (1975) 1163-1174
26. Peng L. Asymptotically unbiased estimators for the extreme-value index. Statist. Probab. Lett. 38 (1998) 107-115
27. Peng L., and Qi Y. Estimating the first- and second-order parameters of a heavy-tailed distribution. Austral. New-Zealand J. Statist. 46 2 (2004) 305-312
28. Pickands J. Statistical inference using extreme order statistics. Ann. Statist. 3 (1975) 119-131
29. Reiss R.-D. Approximate Distributions of Order Statistics. Springer Series in Statistics (1989), Springer, New York
30. Segers J. Generalized Pickands estimators for the extreme value index. J. Statist. Plann. Inference 28 (2005) 381-396
31. Smith R.L. Estimating tails of probability distributions. Ann. Statist. 15 (1987) 1174-1207
32. van der Vaart A. Asymptotic Statistics (1998), Cambridge University Press, Cambridge
33. Weissman I. Estimation of parameters and larger quantiles based on the k largest observations. J. Amer. Statist. Assoc. 73 (1978) 812-815