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Bootstrapping extremes of random variables under power normalization. (English) Zbl 1131.62039
Summary: This paper deals with the asymptotics of bootstrap for the distribution of extremes under power normalization when the underlying distribution belongs to the domain of attraction of an extreme value distribution. We obtained inconsistency, weak consistency and strong consistency of bootstrapping with appropriate choice of the resample size when the normalizing constants are known. The same problems are investigated when the normalizing constants are unknown. The bootstrap for the joint distributions and the confidence intervals for the upper end of the distribution function \(F\) are obtained.

MSC:
62G20 Asymptotic properties of nonparametric inference
62G32 Statistics of extreme values; tail inference
62G09 Nonparametric statistical resampling methods
60F05 Central limit and other weak theorems
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