This paper reviews important concepts and methods that are useful for hypothesis testing.First, we discuss the Neyman-Pearson framework. Various approaches to optimalityare presented, including finite-sample and large-sample optimality. Then, some of the mostimportant methods are summarized, as...

Consider the problem of testing s hypotheses simultaneously. In order to deal with themultiplicity problem, the classical approach is to restrict attention to procedures that controlthe familywise error rate (FWE). Typically, it is known how to construct tests of the individualhypotheses, and...

Consider the problem of testing s hypotheses simultaneously. In this paper, we derivemethods which control the generalized familywise error rate given by the probability ofk or more false rejections, abbreviated k-FWER. We derive both single-step and stepdownprocedures that control the k-FWER in...