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

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Abstract

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.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages25
Volume2003-132
Publication statusPublished - 2003

Publication series

NameCentER Discussion Paper
Volume2003-132

Fingerprint

Extreme Value Index
Random Element
Empirical Process
Domain of Attraction
Extreme Values
Strengthening
Limiting Distribution
Weak Convergence
Asymptotic Normality
Gaussian Process
Tail
Continuous Function
Estimator

Keywords

  • estimation
  • infinite dimensional systems
  • convergence
  • statistics

Cite this

Einmahl, J. H. J., & Lin, T. (2003). Asymptotic Normality of Extreme Value Estimators on C[0,1]. (CentER Discussion Paper; Vol. 2003-132). Tilburg: Econometrics.
Einmahl, J.H.J. ; Lin, T. / Asymptotic Normality of Extreme Value Estimators on C[0,1]. Tilburg : Econometrics, 2003. (CentER Discussion Paper).
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abstract = "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.",
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Einmahl, JHJ & Lin, T 2003 'Asymptotic Normality of Extreme Value Estimators on C[0,1]' CentER Discussion Paper, vol. 2003-132, Econometrics, Tilburg.

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

Tilburg : Econometrics, 2003. (CentER Discussion Paper; Vol. 2003-132).

Research output: Working paperDiscussion paperOther research output

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AU - Lin, T.

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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.

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KW - infinite dimensional systems

KW - convergence

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M3 - Discussion paper

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CY - Tilburg

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Einmahl JHJ, Lin T. Asymptotic Normality of Extreme Value Estimators on C[0,1]. Tilburg: Econometrics. 2003. (CentER Discussion Paper).