Multiple Testing of General Contrasts Using Logical Constraints and Correlations

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Abstract
Use of logical constraints among hypotheses and correlations among test statistics can greatly improve the power of step-down tests. An algorithm for uncovering these logically constrained subsets in a given dataset is described. The multiple testing results are summarized using adjusted p values, which incorporate the relevant dependence structures and logical constraints. These adjusted p values are computed consistently and efficiently using a generalized least squares hybrid of simple and control-variate Monte Carlo methods, and the results are compared to alternative stepwise testing procedures.

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