Sequential Selection Procedures and False Discovery Rate Control
arXiv:1309.5352
Abstract
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,\dots,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 using recent results on p-values in sequential model selection settings.
31 pages, 14 figures. Accepted to the Journal of the Royal Statistical Society: Series B
References in corpus (9)
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Cited by in corpus (7)
- Selective Sequential Model Selection
- On Online Control of False Discovery Rate
- Discussion: "A significance test for the lasso"
- False Discoveries Occur Early on the Lasso Path
- SLOPE is Adaptive to Unknown Sparsity and Asymptotically Minimax
- Accumulation tests for FDR control in ordered hypothesis testing
- A Sparse Linear Model and Significance Test for Individual Consumption Prediction