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Asymptotic normality of extreme value estimators on $C[0,1]$
John H. J. Einmahl, Tao Lin · 2006-05-23 · via math.ST updates on arXiv.org

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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