On the Structure of Multiple Testing Procedures


The field of "multiple hypothesis testing" has traditionally focused on defining and estimating various error measures based on the p-values individually obtained from each test. In this paper we discuss common structure present in typical multiple testing procedures. We introduce "single thresholding procedures" (STPs), a large class of multiple testing procedures encompassing the majority of those used in practice. We propose new concepts of significance for STPs, eliminating the intermediate step of calculating p-values for each test individually. With these developments, it is straightforward to consider the optimality of STPs and show that many complicated procedures actually reduce to a STP. As a specific example, we show that single-stage multiple hypothesis testing procedures are optimal over their corresponding multiple-stage procedures, an open question of much interest in the genomics field.


Biostatistics | Multivariate Analysis | Statistical Methodology | Statistical Theory

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