Bias-reduced extreme quantile estimators of Weibull tail-distributions

Journal of Statistical Planning and Inference

Volumn 138, Issue 5, 2008, Pages 1389-1401

  Diebolt, Jean ^a   Gardes, Laurent ^b   Girard, Stéphane ^b   Guillou, Armelle ^c  

^a CNRS   (France)

^b INRIA RHÔNE ALPES   (France)

^c SORBONNE UNIVERSITÉ   (France)

Author keywords

Asymptotic normality; Bias reduction; Extreme quantile; Least squares approach; Weibull tail distribution

Indexed keywords

EID: 38349019581     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2007.04.025     Document Type: Article

References (24)

1. Beirlant J., Broniatowski M., Teugels J.L., and Vynckier P. The mean residual life function at great age: applications to tail estimation. J. Statist. Plann. Inference 45 (1995) 21-48
2. Beirlant J., Teugels J., and Vynckier P. Practical Analysis of Extreme Values (1996), Leuven University Press, Leuven
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 Starica C. On exponential representations of log-spacings of extreme order statistics. Extremes 5 (2002) 157-180
5. Beirlant J., Bouquiaux C., and Werker B. Semiparametric lower bounds for tail index estimation. J. Statist. Plann. Inference 136 (2006) 705-729
6. Breiman L., Stone C.J., and Kooperberg C. Robust confidence bounds for extreme upper quantiles. J. Comput. Statist. Simulation 37 (1990) 127-149
7. Broniatowski M. On the estimation of the Weibull tail coefficient. J. Statist. Plann. Inference 35 (1993) 349-366
8. Davison A., and Smith R. Models for exceedances over high thresholds. J. Roy. Statist. Soc. Ser. B 52 (1990) 393-442
9. Diebolt J., El-Aroui M., Garrido M., and Girard S. Quasi-conjugate Bayes estimates for GPD parameters and application to heavy tails modelling. Extremes 8 (2005) 57-78
10. Diebolt, J., Gardes, L., Girard, S., Guillou, A., 2007. Bias-reduced estimators of the Weibull-tail coefficient. Test, to appear.
11. Ditlevsen O. Distribution arbitrariness in structural reliability. Structural Safety and Reliability (1994), Balkema, Rotterdam 1241-1247
12. Drees H. On smooth statistical tail functionals. Scand. J. Statist. 25 (1998) 187-210
13. Embrechts P., Klüppelberg C., and Mikosch T. Modelling Extremal Events (1997), Springer, Berlin
14. Feuerverger A., and Hall P. Estimating a tail exponent by modelling departure from a pareto distribution. Ann. Statist. 27 (1999) 760-781
15. Gardes L., and Girard S. Estimating extreme quantiles of Weibull tail-distributions. Comm. Statist. Theory Methods 34 (2005) 1065-1080
16. Gardes L., and Girard S. Comparison of Weibull tail-coefficient estimators. REVSTAT Statist. J. 4 (2006) 163-188
17. Geluk, J.L., de Haan, L., 1987. Regular Variation, Extensions and Tauberian Theorems. In: Math Centre Tracts, vol. 40. Centre for Mathematics and Computer Science, Amsterdam.
18. Girard S. A Hill type estimate of the Weibull tail-coefficient. Comm. Statist. Theory Methods 33 (2004) 205-234
19. de Haan L., and Rootzén H. On the estimation of high quantiles. J. Statist. Plann. Inference 35 (1993) 1-13
20. Hall P., and Welsh A.H. Adaptive estimates of parameters of regular variation. Ann. Statist. 13 (1985) 331-341
21. Hosking J., and Wallis J. Parameter and quantile estimation for the generalized Pareto distribution. Technometrics 29 (1987) 339-349
22. Matthys G., Delafosse E., Guillou A., and Beirlant J. Estimating catastrophic quantile levels for heavy-tailed distributions. Insurance Math. Econom. 34 (2004) 517-537
23. Smith J. Estimating the upper tail of flood frequency distributions. Water Resources Res. 23 (1991) 1657-1666
24. Weissman I. Estimation of parameters and large quantiles based on the k largest observations. J. Amer. Statist. Assoc. 73 (1978) 812-815