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.
@article{1176325769,
author = {Hall, Peter and Mammen, Enno},
title = {On General Resampling Algorithms and their Performance in Distribution Estimation},
journal = {Ann. Statist.},
volume = {22},
number = {1},
year = {1994},
pages = { 2011-2030},
language = {en},
url = {http://dml.mathdoc.fr/item/1176325769}
}
Hall, Peter; Mammen, Enno. On General Resampling Algorithms and their Performance in Distribution Estimation. Ann. Statist., Tome 22 (1994) no. 1, pp. 2011-2030. http://gdmltest.u-ga.fr/item/1176325769/