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.
"On General Resampling Algorithms and their Performance in Distribution Estimation." Ann. Statist. 22 (4) 2011 - 2030, December, 1994. https://doi.org/10.1214/aos/1176325769