Simes inequality
= Simes inequality
{c}
{title2=$\Pr(\min_i p_{(i)}/i\le\alpha/m)\le\alpha$}
For $m\ge1$ independent valid null <p-values>, the displayed inequality follows by applying the <Benjamini-Hochberg procedure> with all nulls true. Its <false discovery rate> then equals the <probability> of at least one rejection. Valid means $\Pr(p_i\le t)\le t$ for $0\le t\le1$; independence is a sufficient hypothesis, and arbitrary dependence is not covered by this proof.