Sequential Bonferroni Methods for Multiple Hypothesis Testing with Strong Control of Family-Wise Error Rates I and II

Sequential procedures are developed for simultaneous testing of multiple hypotheses in sequential experiments. Proposed stopping rules and decision rules achieve strong control of both family-wise error rates I and II. The optimal procedure is sought that minimizes the expected sample size under these constraints. Bonferroni methods for multiple comparisons are extended to sequential setting and are shown to attain an approximately 50% reduction in the expected sample size compared with the earlier approaches. Asymptotically optimal procedures are derived under Pitman alternative.