Speaker
Description
In this talk, we will explore the relationship between the closed testing principle for multiple tests with family-wise error rate (FWER) control and the partitioning plus projection principle for constructing simultaneous confidence intervals. Starting with the simple observation that a multiple test with FWER control is formally equivalent to a one-sided simultaneous confidence interval for the vector of binary parameters indicating the true null and alternative hypotheses, we will see that the closed testing principle can be understood as a special case of the partitioning plus projection principle. We will then utilise this relationship to extend some common closed testing procedures to simultaneous confidence intervals, referencing the existing literature on compatible and informative simultaneous confidence intervals. Another key contribution of our talk and research is the extension of the concept of consonance for closed tests to the partitioning plus projection principle, with the aim of deriving computationally efficient algorithms for calculating simultaneous confidence intervals. These relationships and extensions will be illustrated using simple, instructive examples.
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