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Abstract:
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To strongly control the familywise error rate in multiple testing problems, many procedures in various forms have been proposed. Their underlying theoretic foundation is primarily built on two principles: the closure principle and the partitioning principle. The essence of these two principles is based on parameter space partitioning. In reality, however, certain logical relationships usually exist among null hypotheses to be tested. Several specific testing procedures such as gate-keeping procedure, tree-structured procedure, multi-stage procedure, mixture procedure, and graphical approach have been proposed to address this issue. In this paper, we propose a new approach termed the Covering Principle from the perspective of rejection region coverage analysis. The Covering Principle tackles the multiplicity issue by dividing a whole family of individual null hypotheses into a few disjoint sub-families, for which either the closure principle or the partitioning principle can be utilized.
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