Geodesic
Comparison at optimal levels of classical tail index estimators: a challenge for reduced-bias estimation?
Discussiones Mathematicae. Probability and Statistics, Tome 30 (2010) no. 1, pp. 35-51

Voir la notice de l'article provenant de la source Library of Science

In this article, we begin with an asymptotic comparison at optimal levels of the so-called "maximum likelihood" (ML) extreme value index estimator, based on the excesses over a high random threshold, denoted PORT-ML, with PORT standing for peaks over random thresholds, with a similar ML estimator, denoted PORT-MP, with MP standing for modified-Pareto. The PORT-MP estimator is based on the same excesses, but with a trial of accommodation of bias on the Generalized Pareto model underlying those excesses. We next compare the behaviour of these ML implicit estimators with the equivalent behaviour of a few explicit tail index estimators, the Hill, the moment, the generalized Hill and the mixed moment. As expected, none of the estimators can always dominate the alternatives, even when we include second-order MVRB tail index estimators, with MVRB standing for minimum-variance reduced-bias. However, the asymptotic performance of the MVRB estimators is quite interesting and provides a challenge for a further study of these MVRB estimators at optimal levels.
Keywords: statistics of extremes, semi-parametric estimation, bias estimation, heavy tails, optimal levels 
@article{DMPS_2010_30_1_a2,
     author = {Gomes, M. and Henriques-Rodrigues, L{\'\i}gia},
     title = {Comparison at optimal levels of classical tail index estimators: a challenge for reduced-bias estimation?},
     journal = {Discussiones Mathematicae. Probability and Statistics},
     pages = {35--51},
     publisher = {mathdoc},
     volume = {30},
     number = {1},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMPS_2010_30_1_a2/}
}
TY  - JOUR
AU  - Gomes, M.
AU  - Henriques-Rodrigues, Lígia
TI  - Comparison at optimal levels of classical tail index estimators: a challenge for reduced-bias estimation?
JO  - Discussiones Mathematicae. Probability and Statistics
PY  - 2010
SP  - 35
EP  - 51
VL  - 30
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMPS_2010_30_1_a2/
LA  - en
ID  - DMPS_2010_30_1_a2
ER  - 
%0 Journal Article
%A Gomes, M.
%A Henriques-Rodrigues, Lígia
%T Comparison at optimal levels of classical tail index estimators: a challenge for reduced-bias estimation?
%J Discussiones Mathematicae. Probability and Statistics
%D 2010
%P 35-51
%V 30
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMPS_2010_30_1_a2/
%G en
%F DMPS_2010_30_1_a2
Gomes, M.; Henriques-Rodrigues, Lígia. Comparison at optimal levels of classical tail index estimators: a challenge for reduced-bias estimation?. Discussiones Mathematicae. Probability and Statistics, Tome 30 (2010) no. 1, pp. 35-51. http://geodesic.mathdoc.fr/item/DMPS_2010_30_1_a2/