ABSTRACT
Statisticians have long been faced with settings that have required the simultaneous testing of many different hypotheses. Decision theory depends on the specification of a loss function. One then attempts to find procedures that perform well relative to expected loss. Decision theory for testing a single hypothesis is well established. It is much less so for multiple testing. For testing a single hypothesis, the classical loss function leads to a focus on the standard notions of Types I and II errors. The vast majority of multiple test procedure (MTP) research has focused on achieving high power while controlling either the familywise error rate (FWER) or the false discovery rate (FDR). Both the FWER and FDR type approaches are in the spirit of size and power considerations for testing a single hypothesis. FWER and FDR are global criteria and not really tied to loss functions for individual testing problems. However, every MTP does generate an individual test for each testing problem. This allows MTP performance to be evaluated through the study (and implications) of decision theoretic issues surrounding these individual tests.
