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

Abstract

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.

Keywords:

• Asymptotic optimality
• Family wise error rate
• Multiple comparisons
• Pitman alternative
• Sequential probability ratio test
• Stopping rule

Subject Classifications:

• 62L
• 62F03
• 62F05
• 62H15

ACKNOWLEDGMENTS

This research was supported by the National Science Foundation grant DMS 1007775. Research of the second author was partially supported by the National Security Agency grant H98230-11-1-0147. We thank the associate editor and Professor Mukhopadhyay for their help and attention to our work.

Notes

Recommended by N. Mukhopadhyay