Hochberg procedure

Order $m$ p-values and reject the first $r$ hypotheses, where $r=\max \{j:p_{(j)}\le \alpha /(m-j+1)\}$, with $r=0$ for an empty set. Under independent valid true-null p-values, this step-up procedure controls the familywise error rate. One proof embeds its rejections in the closed testing procedure with Simes tests: every intersection containing a rejected hypothesis passes its local Simes test, so closed-testing control of the familywise error rate applies.