Quasi-conjugate bayes estimates for GPD parameters and application to heavy tails modelling

Extremes

Volumn 8, Issue 1-2, 2005, Pages 57-78

  Diebolt, Jean ^a   El Aroui, Mhamed Ali ^b   Garrido, Myriam ^c   Girard, Stéphane ^d  

^a CNRS   (France)

^b UNIVERSITY OF TUNIS   (Tunisia)

^c ENAC   (France)

^d UNIV GRENOBLE ALPES   (France)

Author keywords

Extreme quantiles; Gamcon II distribution; Generalized Pareto distribution; Gibbs sampler; Peaks over thresholds (POT)

Indexed keywords

EID: 30444434892     PISSN: 13861999     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10687-005-4860-9     Document Type: Article

References (32)

1. Bacro, J. and Brito, M., "Strong limiting behaviour of a simple tail Pareto-index estimator," Stat. Dec. 3, 133-143, (1993).
2. Balkema, A. and de Haan, L., "Residual life time at a great age," Ann. Probab. 2, 792-804, (1974).
3. Beirlant, J. and Teugels, J., "Asymptotic normality of Hill's estimator," in Extreme Value Theory (J. Hüsler and R.D. Reiss, eds), Proceedings of the Oberwolfach Conference, 1987, Springer-Verlag, New York, 1989.
4. Beirlant, J., Dierckx, G., and Guillou, A., Estimation of the Extreme Value Index and Regression on Generalized Quantile Plots, Preprint, Catholic University of Leuven, Catholic University of Leuven, Belgium, 2001.
5. Bottolo, L., Consonni, G., Dellaportas, P., and Lijoi, A., "Bayesian analysis of extreme values by mixture modeling," Extremes 6, 25-47, (2003).
6. Breiman, L., Stone, C., and Kooperberg, C., "Robust confidence bounds for extreme upper quantiles," J. Stat. Comput. Simul. 37, 127-149, (1990).
7. Caers, J., Beirlant, J., and Vynckier, P., "Bootstrap confidence intervals for tail indices," Comput. Stat. Data Anal. 26, 259-277, (1998).
8. Castillo, E. and Hadi, A., "Fitting the Generalized Pareto Distribution to data," J. Am. Stat. Assoc. 92(440), 1609-1620, (1997).
9. Coles, S., An Introduction to Statistical Modelling of Extreme Values. Springer Series in Statistics, 2001.
10. Coles, S. and Powell, E., "Bayesian methods in extreme value modelling: A review and new developments," Int. Stat. Rev. 64(1), 119-136, (1996).
11. Coles, S. and Tawn, J., "A Bayesian analysis of extreme rainfall data," Appl. Stat. 45(4), 463-478, (1996).
12. Damsleth, E., "Conjugate classes of Gamma distributions," Scand. J. Stat.: Theory Appl. 2, 80-84, (1975).
13. Davison, A. and Smith, R., "Models for exceedances over high thresholds," J. R. Stat. Soc., B. 52(3), 393-442, (1990).
14. Dekkers, A., Einmahl, J.H.J., and de Haan, L., "A moment estimator for the index of an extreme-value distribution," Ann. Stat. 17(4), 1833-1855, (1989).
15. Dieboll, J., Guillou, A., and Worms, R., "Asymptotic behaviour of the probability-weighted moments and penultimate approximation," ESAIM, Probab. Stat. 7, 219-238, (2003).
16. Embrechts, P., Klǔppelberg, C., and Mikosch, T., Modelling Extremal Events. Springer, 1997.
17. Garrido, M., Modélisation des évènements rares et estimation des quantiles extrêmes, Méthodes de sèlection de modéles puor les queues de distribution. PhD thesis, Université Joseph Fourier de Grenoble (France), 2002.
18. Grimshaw, S., "Computing maximum likelihood estimates for the Generalized Pareto Distribution," Technometrics 35(2), May, 185-191, (1993).
19. Haeusler, E. and Teugels, J., "On asymptotic normality of Hill's estimator for the exponent of regular variation," Ann. Stat. 13(2), 743-756, (1985).
20. Hill, B., "A simple general approach to inference about the tail of a distribution," Ann. Stat. 3(5), 1163-1174, (1975).
21. Hosking, J. and Wallis, J., "Parameter and quantile estimation for the Generalized Pareto Distribution," Technometrics 29(3), August, 339-349, (1987).
22. Pickands, J., "Statistical inference using extreme order statistics," Ann. Stat, 3, 119-131, (1975).
23. Reiss, R. and Thomas, M., "A new class of Bayesian estimators in paretian excess-of-loss reinsurance," Astin J. 29(2), 339-349, (1999).
24. Reiss, R. and Thomas, M., Statistical Analysis of Extreme Values. Birkhauser Verlag, 2001.
25. Robert, C.P., Discretization and MCMC Convergence Assessment. Lecture Notes in Statistics 135, Springer, 1998.
26. Schnieper, R., "Praktische Erfahrungen mit Grossschadenverteilungen," Mitteil. Schweiz. Verein Versicherungsmath 2, 149-165, (1993).
27. Schultze, J. and Steinebach, J., "On least squares estimates of an exponential tail coefficient," Stat. Decis. 14, 353-372, (1996).
28. Singh, V. and Guo, H., "Parameter estimation for 2-parameter Generalized Pareto Distribution by POME," Stoch. Hydrol. Hydraul. 11(3), 211-227, (1997).
29. Smith, R., "Estimating tails of probability distributions," Ann. Stat. 15(3), 1174-1207, (1987).
30. Smith, R. and Naylor, J., "A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution," Appl. Stat. 36(3), 358-369, (1987).
31. Tancredi, A., Anderson, C., and Ohagan, A., "A Bayesian model for threshold uncertainty in extreme value theory," Working Paper 2002.12, Dipartimento di Scienze Statistiche, Universita di Padova. (2002).
32. Worms, R., "Vitesse de convergence de l'approximation de Pareto Généralisée de la loi des excès," Comptes-Rendus de l'Académie des Sciences, série 1 Tome 333, 65-70, (2001).