### Abstract

Original language | English |
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Place of Publication | Tilburg |

Publisher | Econometrics |

Number of pages | 25 |

Volume | 2003-132 |

Publication status | Published - 2003 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 2003-132 |

### Fingerprint

### Keywords

- estimation
- infinite dimensional systems
- convergence
- statistics

### Cite this

*Asymptotic Normality of Extreme Value Estimators on C[0,1]*. (CentER Discussion Paper; Vol. 2003-132). Tilburg: Econometrics.

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**Asymptotic Normality of Extreme Value Estimators on C[0,1].** / Einmahl, J.H.J.; Lin, T.

Research output: Working paper › Discussion paper › Other research output

TY - UNPB

T1 - Asymptotic Normality of Extreme Value Estimators on C[0,1]

AU - Einmahl, J.H.J.

AU - Lin, T.

N1 - Pagination: 25

PY - 2003

Y1 - 2003

N2 - Consider n i.i.d. random elements on C[0; 1].We show that under an appropriate strengthening of the domain of attraction condition natural estimators of the extreme-value index, which is now a continuous function, and the normalizing functions have a Gaussian process as limiting distribution.A key tool is the weak convergence of a weighted tail empirical process, which makes it possible to obtain the results uniformly on [0; 1].Detailed examples are also presented.

AB - Consider n i.i.d. random elements on C[0; 1].We show that under an appropriate strengthening of the domain of attraction condition natural estimators of the extreme-value index, which is now a continuous function, and the normalizing functions have a Gaussian process as limiting distribution.A key tool is the weak convergence of a weighted tail empirical process, which makes it possible to obtain the results uniformly on [0; 1].Detailed examples are also presented.

KW - estimation

KW - infinite dimensional systems

KW - convergence

KW - statistics

M3 - Discussion paper

VL - 2003-132

T3 - CentER Discussion Paper

BT - Asymptotic Normality of Extreme Value Estimators on C[0,1]

PB - Econometrics

CY - Tilburg

ER -