Consider the multiple testing problem of testing k null hypotheses, where the unknown family of distributions is assumed to satisfy a certain monotonicity assumption. Attention is restricted to procedures that control the familywise error rate in the strong sense and which satisfy a monotonicity condition. Under these assumptions, we prove certain maximin optimality results for some well-known stepdown and stepup procedures.
"On optimality of stepdown and stepup multiple test procedures." Ann. Statist. 33 (3) 1084 - 1108, June 2005. https://doi.org/10.1214/009053605000000066