Asymptotic normality of extreme value estimators on $C[0,1]$

John H. J. Einmahl; Tao Lin

doi:10.1214/009053605000000831

Asymptotic normality of extreme value estimators on $C[0,1]$

Statistics Theory 2007-06-13 v1 Statistics Theory

Authors: John H. J. Einmahl , Tao Lin

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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.

Keywords

extreme value estimators gaussian process domain of attraction weighted tail empirical process c[0,1] asymptotic normality

Cite

@article{arxiv.math/0605612,
  title  = {Asymptotic normality of extreme value estimators on $C[0,1]$},
  author = {John H. J. Einmahl and Tao Lin},
  journal= {arXiv preprint arXiv:math/0605612},
  year   = {2007}
}

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Published at http://dx.doi.org/10.1214/009053605000000831 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Asymptotic normality of extreme value estimators on $C[0,1]$

Abstract

Keywords

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