ON GENERAL RESAMPLING ALGORITHMS AND THEIR PERFORMANCE IN DISTRIBUTION ESTIMATION

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 algor ithms, in a very general setting. Performance is discussed in the cont ext of distribution estimation, and formulae for higher-order moments and cumulants are developed. Arguing thus, necessary and sufficient co nditions are given for general resampling algorithms to correctly capt ure second-order properties.