Stopping time property of thresholds of Storey-type FDR procedures Xiongzhi Chen ∗ and Rebecca W. Doerge † For multiple testing, we introduce Storey-type FDR procedures and the concept of “reg- ular estimator of the proportion of true nulls”. We show that the rejection threshold of a Storey-type FDR procedure is a stopping time with respect to the backward filtration gener- ated by the p-values and that a Storey-type FDR estimator at this rejection threshold equals the pre-specified FDR level, when the estimator of the proportion of true nulls is regular. These results hold regardless of the dependence among or the types of distributions of the p-values. They directly imply that a Storey-type FDR procedure is conservative when the null p-values are independent and uniformly distributed. Keywords : False discovery rate, rejection threshold, stopping time property, Storey-type FDR procedure. MSC 2010 subject classifications : Primary 62C25, 62M99. To control false discovery rate (FDR, Benjamini and Hochberg, 1995) in multiple testing, it is crucial to show the conservativeness of an FDR procedure, i.e., that the FDR of an FDR procedure is no larger than a pre-specified level. To show the conservativeness of their FDR procedures, Storey et al. (2004) used the stopping time property (STP) of the rejection threshold that was claimed in their Lemma 4, and Liang and Nettleton (2012) quoted this lemma as their arXiv:1510.04351v3 [math.ST] 28 Jun 2016 Abstract 1 Introduction $^{∗}$Corresponding author. Center for Statistics and Machine Learning, and Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544. Email: xiongzhi@princeton.edu . $^{†}$Departments of Statistics and Agronomy, Purdue University, West Lafayette, IN 49707. Email: doerge@purdue.edu. 1