Comparison at optimal levels of classical tail index estimators: a challenge for reduced-bias estimation?

M. Ivette Gomes; Lígia Henriques-Rodrigues

Discussiones Mathematicae Probability and Statistics (2010)

  • Volume: 30, Issue: 1, page 35-51
  • ISSN: 1509-9423

Abstract

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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.

How to cite

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M. Ivette Gomes, and Lígia Henriques-Rodrigues. "Comparison at optimal levels of classical tail index estimators: a challenge for reduced-bias estimation?." Discussiones Mathematicae Probability and Statistics 30.1 (2010): 35-51. <http://eudml.org/doc/277076>.

@article{M2010,
abstract = {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.},
author = {M. Ivette Gomes, Lígia Henriques-Rodrigues},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {statistics of extremes; semi-parametric estimation; bias estimation; heavy tails; optimal levels; extremes},
language = {eng},
number = {1},
pages = {35-51},
title = {Comparison at optimal levels of classical tail index estimators: a challenge for reduced-bias estimation?},
url = {http://eudml.org/doc/277076},
volume = {30},
year = {2010},
}

TY - JOUR
AU - M. Ivette Gomes
AU - Lígia Henriques-Rodrigues
TI - Comparison at optimal levels of classical tail index estimators: a challenge for reduced-bias estimation?
JO - Discussiones Mathematicae Probability and Statistics
PY - 2010
VL - 30
IS - 1
SP - 35
EP - 51
AB - 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.
LA - eng
KW - statistics of extremes; semi-parametric estimation; bias estimation; heavy tails; optimal levels; extremes
UR - http://eudml.org/doc/277076
ER -

References

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