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Bootstrap method for central and intermediate order statistics under power normalization. (English) Zbl 1374.62062
The paper concerns bootstrapping for properly standardized central and intermediate order statistics. It has been known that for bootstrapping the distribution of the extremes under the traditional linear normalization of a sample consistently, the bootstrap sample size needs to be of smaller order than the original sample size. In the present paper it is proved that the same is true if we use the bootstrap for estimating a central or an intermediate quantile under power normalization. A simulation study illustrates and supports theoretical results.
62G32 Statistics of extreme values; tail inference
62G09 Nonparametric statistical resampling methods
62G30 Order statistics; empirical distribution functions
60F05 Central limit and other weak theorems
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