Sequential Selection Procedures and False Discovery Rate Control
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 pvalues in sequential model selection settings.
 Publication:

arXiv eprints
 Pub Date:
 September 2013
 arXiv:
 arXiv:1309.5352
 Bibcode:
 2013arXiv1309.5352G
 Keywords:

 Mathematics  Statistics Theory;
 Statistics  Methodology
 EPrint:
 31 pages, 14 figures. Accepted to the Journal of the Royal Statistical Society: Series B