Some Asymptotic Theory for the Bootstrap
Peter J. Bickel, David A. Freedman · The Annals of Statistics · 1981
Efron's "bootstrap" method of distribution approximation is shown to be asymptotically valid in a large number of situations, including $t$-statistics, the empirical and quantile processes, and von Mises functionals. Some counter-examples are also given, to show that the approximation does not always succeed.