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We consider a multiple hypothesis testing setting where the hypotheses areordered and one is only permitted to reject an initial contiguous block,H_1,\dots,H_k, of hypotheses. A rejection rule in this setting amounts to aprocedure for choosing the stopping point k. This setting is inspired by thesequential nature of many model selection problems, where choosing a stoppingpoint or a model is equivalent to rejecting all hypotheses up to that point andnone thereafter. We propose two new testing procedures, and prove that theycontrol the false discovery rate in the ordered testing setting. We also showhow the methods can be applied to model selection using recent results onp-values in sequential model selection settings.

Sequential Selection Procedures and False Discovery Rate Control