Generalized kernel estimators for the Weibull-tail coefficient

Communications in Statistics - Theory and Methods

Volumn 39, Issue 20, 2010, Pages 3695-3716

  Goegebeur, Yuri ^a   Beirlant, Jan ^b   De Wet, Tertius ^c  

^a UNIVERSITY OF SOUTHERN DENMARK   (Denmark)

^b Katholieke Universiteit Leuven   (Belgium)

^c STELLENBOSCH UNIVERSITY   (South Africa)

Author keywords

Kernel statistics; Weibull tail coefficient; Weibull type distribution

Indexed keywords

ASYMPTOTIC NORMALITY; KERNEL ESTIMATORS; KERNEL FUNCTION; KERNEL STATISTICS; L-STATISTICS; ORDER STATISTICS; RANDOM THRESHOLD; REGULARITY CONDITION; SECOND-ORDER CONDITIONS; SIMULATION STUDIES; SMALL SAMPLES; UNDERLYING DISTRIBUTION; WEIBULL; WEIGHTED SUM;

ESTIMATION;

WEIBULL DISTRIBUTION;

EID: 77957167018     PISSN: 03610926     EISSN: 1532415X     Source Type: Journal    
DOI: 10.1080/03610920903324882     Document Type: Article

References (17)

1. Beirlant, J., Broniatowski, M., Teugels, J. L., Vynckier, P. (1995). The mean residual life function at great age: applications to tail estimation. J. Statist. Plann. Infer. 45:21-48.
2. Bingham, N. H., and Goldie., C. M., Teugels, J. L. (1987). Regular Variation. Cambridge: Cambridge University Press.
3. Broniatowski, M. (1993). On the estimation of the Weibull tail coefficient. J. Statist. Plann. Infer. 35:349-366.
4. Chernoff, H., and Gastwirth., J. L., Johns, M. V. (1967). Asymptotic distribution of linear combinations of functions of order statistics with applications to estimation. Ann. Mathemat. Statist. 38:52-72.
5. Ciuperca, G., Mercadier, C. (2008). Semi-parametric estimation for heavy tailed distributions. Extremes 13:55-87.
6. de Haan, L., Ferreira, A. (2006). Extreme Value Theory: An Introduction. New York: Springer.
7. Diebolt, J., Gardes, L., Girard, S., Guillou, A. (2008). Bias-reduced estimators of the Weibull tail-coefficient. Test 17:311-331.
8. Gardes, L., Girard, S. (2005). Estimating extreme quantiles of Weibull tail distributions. Commun. Statist. Theor. Meth. 34:1065-1080.
9. Gardes, L., Girard, S. (2006). Comparison of Weibull tail-coefficient estimators. REVSTAT Statist. J. 4:163-188.
10. Gardes, L., Girard, S. (2008). Estimation of the Weibull-tail coefficient with linear combination of upper order statistics. J. Statist. Plann. Infer. 138:1416-1427.
11. Geluk, J., de Haan, L. (1987). Regular Variation, Extensions and Tauberian Theorems. Amsterdam: CWI Tract 40, Center for Mathematics and Computer Science.
12. Girard, S. (2004). A Hill type estimator of the Weibull tail coefficient. Commun. Statist. Theor. Meth. 33:205-234.
13. Goegebeur, Y., Guillou, A. (2009). Goodness-of-fit testing for Weibull-type behavior. J. Statist. Plann. Infer. 140:1417-1436.
14. Gomes, M. I., Martins, M. J. (2001). Generalizations of the Hill estimator - asymptotic versus finite sample behaviour. J. Statist. Plann. Infer. 93:161-180.
15. Mason, D. M. (1981). Asymptotic normality of linear combinations of order statistics with a smooth score function. Ann. Statist. 9:899-908.
16. Rényi, A. (1953). On the theory of order statistics. Acta Mathematica Academiae Scientiarum Hungaricae 4:191-231.
17. Segers, J. (2001). Residual estimators. J. Statist. Plann. Infer. 98:15-27.