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Some results on the influence of extremes on the bootstrap. (English) Zbl 0774.62042
For a random sample of size \(n\), the authors consider the problems of bootstrapping consistently (i) the sample maximum, (ii) intermediate trimmed means where the trimming proportions are \(o(n)\), and (iii) the sample mean where the population is in the domain of attraction of a stable law. While doing so, they explore the influence of the extreme order statistics on bootstrapping (ii) and (iii), and establish some interconnections between the normalizing constants. The proofs depend heavily on empirical process methodology developed by the authors and their coworkers.

MSC:
62G09 Nonparametric statistical resampling methods
60G70 Extreme value theory; extremal stochastic processes
62G30 Order statistics; empirical distribution functions
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