Geodesic
Bootstrap method for central and intermediate order statistics under power normalization
Kybernetika, Tome 51 (2015) no. 6, pp. 923-932.

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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.
DOI : 10.14736/kyb-2015-6-0923
Classification : 62F40, 62G32
Keywords: bootstrap technique; power normalization; weak consistency; central order statistics; intermediate order statistics 
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Barakat, H. M.; Nigm, E. M.; Khaled, O. M. Bootstrap method for central and intermediate order statistics under power normalization. Kybernetika, Tome 51 (2015) no. 6, pp. 923-932. doi : 10.14736/kyb-2015-6-0923. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2015-6-0923/

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