Reduced-bias tail index estimation and the jackknife methodology
Article first published online: 4 MAY 2007
Volume 61, Issue 2, pages 243–270, May 2007
How to Cite
Gomes, M. I., Miranda, C. and Viseu, C. (2007), Reduced-bias tail index estimation and the jackknife methodology. Statistica Neerlandica, 61: 243–270. doi: 10.1111/j.1467-9574.2007.00346.x
- Issue published online: 4 MAY 2007
- Article first published online: 4 MAY 2007
- Received: February 2006. Revised: July 2006.
- statistical theory of extremes;
- semi-parametric estimation;
- resampling techniques
In the context of regularly varying tails, we first analyze a generalization of the classical Hill estimator of a positive tail index, with members that are not asymptotically more efficient than the original one. This has led us to propose alternative classical tail index estimators, that may perform asymptotically better than the Hill estimator. As the improvement is not really significant, we also propose generalized jackknife estimators based on any two members of these two classes. These generalized jackknife estimators are compared with the Hill estimator and other reduced-bias estimators available in the literature, asymptotically, and for finite samples, through the use of Monte Carlo simulation. The finite-sample behaviour of the new reduced-bias estimators is also illustrated through a practical example in the field of finance.