### Abstract

Summary: We consider a new class of consistent semi-parametric estimators of a negative extreme value index, based on the set of the $k$ largest observations. This class of estimators depends on a control or tuning parameter, which enables us to have access to an estimator with a null second-order component of asymptotic bias, and with a rather interesting mean squared error, as a function of $k$. We study the consistency and asymptotic normality of the proposed estimators. Their finite sample behaviour is obtained through Monte Carlo simulation.

Original language | Unknown |
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Pages (from-to) | 5-19 |

Journal | Discuss. Math., Probab. Stat. |

Volume | 30 |

Issue number | 1 |

Publication status | Published - 1 Jan 2010 |