Title: BONuS: Multiple multivariate testing with a data-adaptive test statistic
Authors: Chiao-Yu Yang - UC Berkeley (United States) [presenting]
Lihua Lei - University of California, Berkeley (United States)
Nhat Pham Minh Ho - University of Texas at Austin (United States)
William Fithian - University of California at Berkeley (United States)
Abstract: A new adaptive empirical Bayes framework is proposed, the Bag-Of-Null-Statistics (BONuS) procedure, for multiple testing where each hypothesis testing problem is itself multivariate or nonparametric. BONuS is an adaptive and interactive knockoff-type method that helps improve the testing power while controlling the false discovery rate (FDR), and is closely connected to the ``counting knockoffs'' procedure. Contrary to procedures that start with a -value for each hypothesis, our method analyzes the entire data set to adaptively estimate an optimal -value transform based on an empirical Bayes model. Despite the extra adaptivity, our method controls FDR in finite samples even if the empirical Bayes model is incorrect or the estimation is poor. An extension, the Double BONuS procedure, validates the empirical Bayes model to guard against power loss due to model misspecification.