Different Types of Optimality in Multiple Testing
Juliet Popper Shaffer
University of California, Berkeley
Even in the test of a single hypothesis there are many types of optimality criteria. The number of possibilities increases greatly in multiple testing. For example, the idea of maximizing power can be generalized as maximizing the probability of one or more rejections of false hypotheses, the probability of rejecting all false hypotheses, the expected number of false hypotheses rejected, the probability of rejecting at least k hypotheses, given that at least k are false, etc.
This talk will review some criteria that have been considered and optimal procedures given those criteria.