Title: Resampling Fewer Than n Observations: Gains, Losses, and Remedies for Losses
Authors: P.J. Bickel, F. Götze, W.R. van Zwet
Date: August 1994
Abstract:
We discuss a number of resampling schemes in which $m=o(n)$ observations are
resampled.  We review nonparametric bootstrap failure and give results old
and new on how the $m$ out of $n$ with replacement bootstraps and without
replacement works.  We extend work of Bickel and Yahav (1988) to show that
$m$ out of $n$ bootstraps can be made second order correct, if the usual
nonparametric bootstrap is correct and study how these extrapolation
techniques work when the nonparametric bootstrap doesn't.