We consider the problem of detecting associations between random vectors of any dimension. Few tests of independence exist that are consistent against all dependent alternatives. We propose a powerful test that is applicable in all dimensions and consistent against all alternatives. The test has...

The linear step-up multiple testing procedure controls the false discovery rate at the desired level q for independent and positively dependent test statistics. When all null hypotheses are true, and the test statistics are independent and continuous, the bound is sharp. When some of the null...

Many studies draw inferences about multiple endpoints but ignore the statistical implications of multiplicity. Effects inferred to be positive when there is no adjustment for multiplicity can lose their statistical significance when multiplicity is taken into account, perhaps explaining why such...