## Abstract

Let {Xn,n⩾1}
be a sequence of independent random variables with common continuous
distribution function F having finite upper endpoint. A new tail index
estimator γ^

Kn(ai,m)=\# {j:X(n−m+:1)−ai<Xj⩽X(n−m+1:n)},m⩾1

where

_{ n }is defined based on only two numbers of near m-extremesKn(ai,m)=\# {j:X(n−m+:1)−ai<Xj⩽X(n−m+1:n)},m⩾1

where

*X*_{ (i:n) }denotes the -th order statistic and*a*_{2}>*a*_{1}> 0. The weak and almost sure convergence of γ^_{ n }to the tail index γ, as well as the asymptotic distribution is given. Moreover, the asymptotic distribution of*K*_{n}*(a*_{n}*, m)*for*a*_{n}*→ 0*is derived.Original language | English |
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Pages (from-to) | 197-210 |

Number of pages | 14 |

Journal | Methodology and Computing in Applied Probability |

Volume | 5 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jun 2003 |

Externally published | Yes |

## Keywords

- extreme value theory
- near extremes
- tail index estimation