In this paper, we compare the asymptotic behavior of some common
block bootstrap methods based on nonrandom as well as random block lengths. It
is shown that, asymptotically, bootstrap estimators derived using any of the
methods considered in the paper have the same amount of bias to the
first order. However, the variances of these bootstrap estimators may be
different even in the first order. Expansions for the bias, the variance and
the mean-squared error of different block bootstrap variance estimators are
obtained. It follows from these expansions that using overlapping blocks is to
be preferred over nonoverlapping blocks and that using random block lengths
typically leads to mean-squared errors larger than those for nonrandom block
lengths.