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

Keywords

  • estimation
  • infinite dimensional systems
  • convergence
  • statistics

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