Bias reduction in risk modelling: Semi-parametric quantile estimation

Test

Volumn 15, Issue 2, 2006, Pages 375-396

  Gomes, M Ivette ^a   Figueiredo, Fernanda ^b  

^a UNIVERSITY OF LISBON   (Portugal)

^b UNIVERSITY OF PORTO   (Portugal)

Author keywords

Bias reduction; Heavy tails; High quantiles; Semi parametric estimation; Statistics of extremes

Indexed keywords

EID: 33845642085     PISSN: 11330686     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02607058     Document Type: Article

References (19)

1. BEIRLANT, J., DIERCKX, G., GOEGEBUUR, Y., and MATTHYS, G. (1999). Tail index estimation and an exponential regression model. Extremes, 2:177-200.
2. CAEIRO, F. and GOMES, M. I. (2002a). A class of asymptotically unbiased semi-parametric estimators of the tail index. Test, 11(2):345-364.
3. CAEIRO, F. and GOMES, M.I. (2002b). Bias reduction in the estimation of parameters of rare events. Theory of Stochastic Processes, 8:67-76.
4. DE HAAN, L. and ROOTZÉN, H. (1993). On the estimation of high quaritiles. Journal of Statistical Planning and Inference, 35:1-13.
5. DEKKERS, A. L. M., EINMAHL, J. H. J., and DE HAAN, L. (1989). A moment estimator for the index of an extreme-value distribution. The Annals of Statistics, 17:1833-1855.
6. FERREIRA, A., DE HAAN, L., and PENG, L. (2003). On optimising the estimation of high quantiles of a probability distribution. Statistics, 37:401-434.
7. FEUERVERGER, A. and HALL, P. (1999). Estimating a tail exponent by modelling departure from a Pareto distribution. The Annals of Statistics, 27:760-781.
8. FRAGA ALVES, M. I., GOMES, M. I., and DE HAAN, L. (2003). A new class of semi-parametric estimators of the second order parameter. Portugaliae Mathematica, 60:194-213.
9. GALAMBOS, J. (1987). The Asymptotic Theory of Extreme Order Statistics. Robert E. Krieger Publishing Co., Melbourne, FL, 2nd ed.
10. GELUK, J. and DE HAAN, L. (1987). Regular Variation, Extensions and Tauberian Theorems. Center for Mathematics and Computer Science, Amsterdam.
11. GOMES, M. I. and MARTINS, M. J. (2001). Alternatives to Hill's estimator - asymptotic versus finite sample behaviour. Journal of Statistical Planning and Inference, 93:161-180.
12. GOMES, M. I. and MARTINS, M. J. (2002). "Asymptotically unbiased" estimators of the tail index based on external estimation of the second order parameter. Extremes, 5:5-31.
13. GOMES, M. I. and MARTINS, M. J. (2004). Bias reduction and explicit semi-parametric estimation of the tail index. Journal of Statistical Planning and Inference, 124:361-378.
14. GOMES, M. I., MARTINS, M. J., and NEVES, M. (2000). Alternatives to a semi-parametric estimator of parameters of rare events - the Jackknife methodology. Extremes, 3:207-229.
15. GOMES, M. I. and OLIVEIRA, O. (2001). The bootstrap methodology in Statistical Extremes - choice of the optimal sample fraction. Extremes, 4:331-358.
16. HALL, P. and WELSH, A. H. (1985). Adaptive estimates of parameters of regular variation. The Annals of Statistics, 13:331-341.
17. HILL, B. (1975). A simple general approach to inference about the tail of a distribution. The Annals of Statistics, 3:1163-1174.
18. MATTHYS, G. and BEIRLANT, J. (2003). Estimating the extreme value index and high quantiles with exponential regression models. Statistica Sinica, 13:853-880.
19. WEISSMAN, I. (1978). Estimation of parameters and large quantiles based on the k largest observations. Journal of the American Statistical Association, 73:812-815.