摘要：We consider two popular, permutation-based, step-down procedures of $p$-values adjustment in multiple testing problems known as min $P$ and max $T$ and intended for strong control of the family-wise error rate, under the so-called subset pivotality property (SPP). We examine key but subtle issues involved in ascertaining validity of these methods, and also introduce a new, slightly narrower notion of strong control which ensures proper bounds on the family-wise error rate in min $P$ and max $T$ without SPP.
关键词：multiple testing; strong control of family-wise error rate; step down p-value adjustment methods; subset pivotality property; permutation test
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