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Sequential selection procedures and false discovery rate control
Author(s) -
G'Sell Max Grazier,
Wager Stefan,
Chouldechova Alexandra,
Tibshirani Robert
Publication year - 2016
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12122
Subject(s) - selection (genetic algorithm) , false discovery rate , multiple comparisons problem , early stopping , computer science , sequential analysis , model selection , control (management) , statistical hypothesis testing , point (geometry) , block (permutation group theory) , algorithm , mathematics , machine learning , statistics , artificial intelligence , combinatorics , biochemistry , chemistry , geometry , artificial neural network , gene
Summary We consider a multiple‐hypothesis testing setting where the hypotheses are ordered and one is only permitted to reject an initial contiguous blockH 1 , … , H kof 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.