## Abstract

The main objective of statistics of extremes is the prediction of rare events, and its primary problem has been the estimation of the extreme value index (EVI). Whenever we are interested in large values, such estimation is usually performed on the basis of the largest k + 1 order statistics in the sample or on the excesses over a high level u. The question that has been often addressed in practical applications of extreme value theory is the choice of either k or u, and an adaptive EVI-estimation. Such a choice can be either heuristic or based on sample paths stability or on the minimization of a mean squared error estimate

as a function of k. Some of these procedures will be reviewed. Despite of the

fact that the methods provided can be applied, with adequate modifications, to any real EVI and not only to the adaptive EVI-estimation but also to the adaptive estimation of other relevant right-tail parameters, we shall illustrate the methods essentially for the EVI and for heavy tails, i.e., for a positive EVI.

as a function of k. Some of these procedures will be reviewed. Despite of the

fact that the methods provided can be applied, with adequate modifications, to any real EVI and not only to the adaptive EVI-estimation but also to the adaptive estimation of other relevant right-tail parameters, we shall illustrate the methods essentially for the EVI and for heavy tails, i.e., for a positive EVI.

Original language | English |
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Title of host publication | Extreme Value Modeling and Risk Analysis |

Subtitle of host publication | Methods and Applications |

Publisher | Chapman and Hall/CRC 2007 |

Pages | 69-86 |

ISBN (Electronic) | 978-1-4987-0131-0 |

ISBN (Print) | 978-1-4987-0129-7 |

DOIs | |

Publication status | Published - 6 Jan 2016 |

## Keywords

- Bootstrap methodology
- Heuristic methods
- Optimal sample fraction
- Sample-paths stability
- Semi-parametric estimation
- Statistical theory of extremes