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Bootstrap method for central and intermediate order statistics under power normalization

Haroon Mohamed BarakatE. M. NigmO. M. Khaled — 2015


It has been known for a long time 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 this paper, we show 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 corroborates theoretical results.

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