Multiple hypotheses testing and expected number of type I. errors

摘要: The performance of multiple test procedures with respect to error control is an old issue. Assuming that all hypotheses are true we investigate the behavior expected number type I errors (ENE) as a characteristic certain tests controlling familywise error rate (FWER) or the false discovery (FDR) at prespecified level. We derive explicit formulas for distribution rejections well ENE single-step, step-down and step-up based on independent $p$-values. Moreover, determine corresponding asymptotic distributions formulae ENE if tends infinity. In case FWER-control mostly obtain Poisson distributions in one geometric as limiting distributions; FDR which apparently not named literature. Surprisingly, is bounded by small regardless under consideration. Finally, it turns out dependent statistics behaves completely differently compared independent test statistics.