Sequential selection procedures and false discovery rate control

By M. G'Sell, Stefan Wager, Alexandra Chouldechova, Robert Tibshirani. 2013

176 citations recorded by the source corpus.

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.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/905e264286c1b05a1f802659bb075a7cd5274492

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In Statistics and Probability

Citations in the corpus

Multiple testing with the structure‐adaptive Benjamini–Hochberg algorithm (2016, methodology): “In this sense, this version of our method can be viewed as a relaxation of the ordered testing methods of [16, 1, 21].”
SLOPE is Adaptive to Unknown Sparsity and Asymptotically Minimax (2015, background): “Others such as [38] are likely to be far too conservative.”
Breaking the curse of dimensionality in regression (2017, methodology): “In addition, the result above guarantees asymptotic exactness of the proposed GRIP test in a class of high-correlation sparse models where the feature correlation and therefore sparsity of the precision matrix is unrestricted; Javanmard and Montanari (2014a) have a robust test in this setting when t”
Controlling False Discoveries During Interactive Data Exploration (2016, methodology): “The Sequential FDR procedure [15] does not require the sorting of all the hypotheses, but still require to calculate all the tests before their corresponding significance can finalize.”
Exact post-selection inference for the generalized lasso path (2018, background): “[15], to choose a stopping point in the path, with a guarantee on the FDR.”
Selective Sequential Model Selection (2015, methodology): “Recently G’Sell et al. (2013) and Li and Barber (2015) proposed sequential stopping rules of this kind.”
Automated threshold selection for extreme value analysis via ordered goodness-of-fit tests with adjustment for false discovery rate (2018, methodology): “Another stopping rule developed in G’Sell et al. (2016), StrongStop, could be applied in the same manner.”