A class of unbiased location invariant Hill-Type estimators for heavy tailed distributions

Electronic Journal of Statistics

Volumn 2, Issue , 2008, Pages 829-847

  Li, Jiaona ^a   Peng, Zuoxiang ^a   Nadarajah, Saralees ^b  

^a SOUTHWEST UNIVERSITY   (China)

^b UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

Asymptotic normality; Location invariant Hill Type heavy tailed index estimator; Second order regular variation

Indexed keywords

EID: 77954862882     PISSN: 19357524     EISSN: None     Source Type: Journal    
DOI: 10.1214/08-EJS276     Document Type: Article

References (18)

1. Beirlant, J., Dierckx, G., Guillou, A. And Stărică C. (2002). On exponential representions of log-spacings of extreme order statistics. Extremes, 5, 157-180.
2. Caeiro, F. And Gomes, M. I. (2002). A class of asymptotically unbiansed semi-parametric estimators of the tail index. Sociedad de Estadistica e Investigacion Operativa, 11, 345-364.
3. De Haan, L. And Ferreira, A. (2006). Extreme Value Theory. Springer, New York.
4. Dekkers, A. L. M., Einmahl, J. H. J. And de Haan, L. (1989). A moment estimator for the index of an extreme-value distribution. Annals of Statistics, 4, 1833-1855.
5. Embrechets, P., Kluppelberg, C. And Mikosch, T. (1997). Modelling Extremal Events for Insurance and Finance. Springer, New York.
6. Fraga Alves, M. I. (2001). A location invariant Hill-type estimator. Extremes, 4, 199-217.
7. Gomes, M. I., de Haan, L. And Henriques Rodrigues, L. (2008). Tail index estimation through the accomodation of bias in the weighted log-excesses. Journal of the Royal Statistical Society B, 70, 31-53.
8. Gomes, M. I. And Henriques Rodrigues, L. (2008). Tail index estimation for heavy tails: accommodation of bias in the excesses over a high threshold. Extremes, doi 10.1007/-008-0059-1.
9. 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.
10. Gomes, M. I. And Martins, M. J. (2004). Bias reduction and explicit estimation of the tail index. Journal of Statistical Planning Inference, 124, 361-378.
11. Hill, B. M. (1975). A simple general approach to inference about the tail of a distribu-tion. Annals of Statistics, 3, 1163-1174.
12. Ling C. X., Peng, Z. And Nadarajah, S. (2007a). A location invariant moment-type estimator (I). Theory Probability and Mathematical Statistics, 76, 22-30.
13. Ling C. X., Peng, Z. And Nadarajah, S. (2007b). A location invariant moment-type estimator (II). Theory Probability and Mathematical Statistics, 77, 167-178.
14. Peng, L. (1998). Asymptotically unbiased estimator for the extreme-value index. Statistics and Probability Letters, 2, 107-115.
15. Peng, L. And Qi, Y. (2006a). A new calibration method of constructing empirical likelihood-based confidence intervals for the tail index. Australian and New Zealand Journal of Statistics, 48, 59-66.
16. Peng, L. And Qi, Y. (2006b). Confidence regions for high quantiles of a heavy tailed distribution. Annals of Statistics, 4, 1964-1986.
17. Qi, Y. (2008a). On the tail index of a heavy tailed distribution. Annals of the Institute of Statistical Mathematics. To appear.
18. Qi, Y. (2008b). Bootstrap and empirical likelihood methods in extremes. Extremes, doi 10.1007/-007-0049-8.