  We study generalized bootstrap confidence regions for the mean of a random
vector whose coordinates have an unknown dependency structure. The random
vector is supposed to be either Gaussian or to have a symmetric and bounded
distribution. The dimensionality of the vector can possibly be much larger than
the number of observations and we focus on a nonasymptotic control of the
confidence level, following ideas inspired by recent results in learning
theory. We consider two approaches, the first based on a concentration
principle (valid for a large class of resampling weights) and the second on a
resampled quantile, specifically using Rademacher weights. Several intermediate
results established in the approach based on concentration principles are of
interest in their own right. We also discuss the question of accuracy when
using Monte Carlo approximations of the resampled quantities.
