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

The Annals of Statistics · 2006 · Volume 34 · Issue 1

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

60F17, 60G70, 62G05, 62G30, 62G32, estimation, extreme value index, infinite-dimensional extremes, weak convergence on C[0,1]

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