Consistency of the Subsample Bootstrap empirical process |
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Authors: | Markus Pauly |
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Institution: | 1. Institute of Mathematical Statistics and Actuarial Science, University of Bern , Alpeneggstrasse 22, CH-3012 , Bern , Switzerland markus.pauly@stat.unibe.ch |
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Abstract: | In the classical Bootstrap approach the number of distinct observation in the resample is random. To overcome this hitch Rao et al. Bootstrap by sequential resampling, J. Statist. Plan. Inference 64 (1997), pp. 257–281] have proposed a modified resampling procedure – the so-called Sequential Bootstrap or 0.632-Bootstrap – in which each resample has exactly the same number m ~eq ?0.632 n? of distinct observations. Motivated by this idea we introduce an akin procedure, the Subsample Bootstrap, where additionally even the size of each resample is equal. It will turn out that the Subsample Bootstrap empirical process is consistent for a wide class of Donsker classes. |
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Keywords: | bootstrap sequential bootstrap empirical process Donsker classes resampling methods |
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