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

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

2006-05-23

arxiv.org/abs/math/0605612v1

Annals of Statistics 2006, Vol. 34, No. 1, 469-492

Mathematics

Statistics Theory

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

Scientific paper

10.1214/009053605000000831

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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