Multiple testing of one-sided hypotheses: Combining Bonferroni and the bootstrap

In many multiple testing problems, the individual null hypotheses (i) concern univariate parameters and (ii) are one-sided. In such problems, power gains can be obtained for bootstrap multiple testing procedures in scenarios where some of the parameters are "deep in the null" by making certain adjustments to the null distribution under which to resample. In this paper, we compare a Bonferroni adjustment that is based on finite-sample considerations with certain "asymptotic" adjustments previously suggested in the literature.