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December, 1994 On General Resampling Algorithms and their Performance in Distribution Estimation
Peter Hall, Enno Mammen
Ann. Statist. 22(4): 2011-2030 (December, 1994). DOI: 10.1214/aos/1176325769


Recent work of several authors has focussed on first-order properties (e.g., consistency) of general bootstrap algorithms, where the numbers of times that data values are resampled form an exchangeable sequence. In the present paper we develop second-order properties of such algorithms, in a very general setting. Performance is discussed in the context of distribution estimation, and formulae for higher-order moments and cumulants are developed. Arguing thus, necessary and sufficient conditions are given for general resampling algorithms to correctly capture second-order properties.


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Peter Hall. Enno Mammen. "On General Resampling Algorithms and their Performance in Distribution Estimation." Ann. Statist. 22 (4) 2011 - 2030, December, 1994.


Published: December, 1994
First available in Project Euclid: 11 April 2007

zbMATH: 0828.62039
MathSciNet: MR1329180
Digital Object Identifier: 10.1214/aos/1176325769

Primary: 62G05
Secondary: 62G15

Keywords: bootstrap , Cornish-Fisher expansions , cumulant , Distribution estimation , Edgeworth expansion , jackknife , ‎mean‎ , Moment , resample , wild bootstrap

Rights: Copyright © 1994 Institute of Mathematical Statistics


Vol.22 • No. 4 • December, 1994
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