COMPARISON OF BOOTSTRAP AND ASYMPTOTIC APPROXIMATIONS TO THE DISTRIBUTION OF A HEAVY-TAILED MEAN

It is well-know that for heavy-tailed distributions the bootstrap can lead to inconsistent estimation of the distribution of the sample mean ; and that this difficulty may be overcome by using the so-called ''su bsample bootstrap'', where the size of a bootstrap resample is an orde r of magnitude smaller than that of the sample. Naturally, one might a sk whether, as in classical problems, the bootstrap applied to heavy-t ailed distributions produces more accurate approximations to the distr ibution of the sample mean than do asymptotic methods. We show that, g enerally speaking, it does not. In an important class of problems, the subsample bootstrap performs more poorly than asymptotic methods, eve n if the subsample size is chosen optimally. A technique related to Ri chardson extrapolation, effectively a cross between the subsample boot strap and asymptotic methods, performs better than either approach in some, but not all, circumstances.