On some representations of the bootstrap
The bootstrap statistic \({\hat \theta}{}^*_ n-{\hat \theta}_ n\) is represented as the sum of two terms, one of which has the same distribution as \({\hat \theta}{}_ n-\theta\) and the other is a relatively negligible remainder. The representation is then applied to the problems of estimating a distribution and a quantile. The study includes the tail part of the distribution and quantiles for which the convergence rates could be faster than the usual ``\(n^{-1/2}\)'' rate.
scientific article; zbMATH DE number 4076333