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Einmahl, John H. J.; Lin, Tao

Asymptotic normality of extreme value estimators on \(C[0,1]\). (English) Zbl 1091.62041

Ann. Stat. 34, No. 1, 469-492 (2006).
Summary: 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.

Cited in 12 Documents

MSC:

62G32 Statistics of extreme values; tail inference
62F05 Asymptotic properties of parametric tests
62G20 Asymptotic properties of nonparametric inference
62G05 Nonparametric estimation
60G70 Extreme value theory; extremal stochastic processes
60F17 Functional limit theorems; invariance principles

Keywords:

estimation; extreme value index; infinite-dimensional extremes; weak convergence on \(C[0,1]\)
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References:

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