Sequential selection procedures and false discovery rate control

We consider a multiple‐hypothesis testing setting where the hypotheses are ordered and one is only permitted to reject an initial contiguous block H1,…,Hk of hypotheses. A rejection rule in this setting amounts to a procedure for choosing the stopping point k. This setting is inspired by the sequent...

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Published in:	Journal of the Royal Statistical Society. Series B, Statistical methodology Vol. 78; no. 2; pp. 423 - 444
Main Authors:	G'Sell, Max Grazier, Wager, Stefan, Chouldechova, Alexandra, Tibshirani, Robert
Format:	Journal Article
Language:	English
Published:	Oxford Royal Statistical Society 01.03.2016 Blackwell Publishing Ltd John Wiley & Sons Ltd Oxford University Press
Subjects:	Discovery equations False discovery rate Hypotheses Hypothesis testing Multiple-hypothesis testing Rules Selection procedures Sequential testing Statistical analysis Statistics Stopping rule Studies
ISSN:	1369-7412, 1467-9868
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Abstract	We consider a multiple‐hypothesis testing setting where the hypotheses are ordered and one is only permitted to reject an initial contiguous block H1,…,Hk of hypotheses. A rejection rule in this setting amounts to a procedure for choosing the stopping point k. This setting is inspired by the sequential nature of many model selection problems, where choosing a stopping point or a model is equivalent to rejecting all hypotheses up to that point and none thereafter. We propose two new testing procedures and prove that they control the false discovery rate in the ordered testing setting. We also show how the methods can be applied to model selection by using recent results on p‐values in sequential model selection settings.
AbstractList	We consider a multiple-hypothesis testing setting where the hypotheses are ordered and one is only permitted to reject an initial contiguous block H1,…,Hk of hypotheses. A rejection rule in this setting amounts to a procedure for choosing the stopping point k. This setting is inspired by the sequential nature of many model selection problems, where choosing a stopping point or a model is equivalent to rejecting all hypotheses up to that point and none thereafter. We propose two new testing procedures and prove that they control the false discovery rate in the ordered testing setting. We also show how the methods can be applied to model selection by using recent results on p-values in sequential model selection settings. Summary We consider a multiple‐hypothesis testing setting where the hypotheses are ordered and one is only permitted to reject an initial contiguous block H1,…,Hk of hypotheses. A rejection rule in this setting amounts to a procedure for choosing the stopping point k. This setting is inspired by the sequential nature of many model selection problems, where choosing a stopping point or a model is equivalent to rejecting all hypotheses up to that point and none thereafter. We propose two new testing procedures and prove that they control the false discovery rate in the ordered testing setting. We also show how the methods can be applied to model selection by using recent results on p‐values in sequential model selection settings. We consider a multiple-hypothesis testing setting where the hypotheses are ordered and one is only permitted to reject an initial contiguous block H1,..., Hk of hypotheses. A rejection rule in this setting amounts to a procedure for choosing the stopping point k. This setting is inspired by the sequential nature of many model selection problems, where choosing a stopping point or a model is equivalent to rejecting all hypothese up to that point and none thereafter. We propose two new testing procedures and prove that they control the false discovery rate in the ordered testing setting. We also show how the methods can be applied to model selection by using recent results on p-values in sequential model selection settings. Summary We consider a multiple-hypothesis testing setting where the hypotheses are ordered and one is only permitted to reject an initial contiguous block H 1 ,...,H k of hypotheses. A rejection rule in this setting amounts to a procedure for choosing the stopping point k. This setting is inspired by the sequential nature of many model selection problems, where choosing a stopping point or a model is equivalent to rejecting all hypotheses up to that point and none thereafter. We propose two new testing procedures and prove that they control the false discovery rate in the ordered testing setting. We also show how the methods can be applied to model selection by using recent results on p-values in sequential model selection settings.
Author	Wager, Stefan Tibshirani, Robert Chouldechova, Alexandra G'Sell, Max Grazier
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Snippet	We consider a multiple‐hypothesis testing setting where the hypotheses are ordered and one is only permitted to reject an initial contiguous block H1,…,Hk of... We consider a multiple-hypothesis testing setting where the hypotheses are ordered and one is only permitted to reject an initial contiguous block H1,..., Hk... Summary We consider a multiple‐hypothesis testing setting where the hypotheses are ordered and one is only permitted to reject an initial contiguous block... We consider a multiple-hypothesis testing setting where the hypotheses are ordered and one is only permitted to reject an initial contiguous block H1,…,Hk of... Summary We consider a multiple-hypothesis testing setting where the hypotheses are ordered and one is only permitted to reject an initial contiguous block H 1...
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SubjectTerms	Discovery equations False discovery rate Hypotheses Hypothesis testing Multiple-hypothesis testing Rules Selection procedures Sequential testing Statistical analysis Statistics Stopping rule Studies
Title	Sequential selection procedures and false discovery rate control
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