## Abstract

Reduced-bias versions of a very simple generalization of the ‘classical’ Hill estimator of a positive extreme value index (EVI) are put forward. The Hill estimator can be regarded as the logarithm of the mean-of-order-0 of a certain set of statistics. Instead of such a geometric mean, it is sensible to consider the mean-of-order-p (MOP) of those statistics, with p real. Under a third-order framework, the asymptotic behaviour of the MOP, optimal MOP and associated reduced-bias classes of EVI-estimators is derived. Information on the dominant non-null asymptotic bias is also provided so that we can deal with an asymptotic comparison at optimal levels of some of those classes. Large-scale Monte-Carlo simulation experiments are undertaken to provide finite sample comparisons.

Original language | English |
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Pages (from-to) | 561-589 |

Number of pages | 29 |

Journal | Extremes |

Volume | 19 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1 Dec 2016 |

## Keywords

- Bias estimation
- Heavy tails
- Optimal levels
- Semi-parametric reduced-bias estimation
- Statistics of extremes