Multiple Testing of One-Sided Hypotheses under Unknown Dependence

The one-sided hypotheses in a multiple testing problem make the empirical null distribution (or p-values) conservative.Furthermore, it introduces a significant loss of power if not appropriately considered.We propose a multiple testing procedure named discarding adaptively with bounding on principal factor approximation (DAB-PFA) to simultaneously test a number of one-sided hypotheses under the general dependency of test statistics.Specifically, we use the principal factor approximation (PFA) by Fan and Han (2017) to account for the dependence structure among test statistics and adaptively discard small or large p-values when estimating the realized false discovery proportion (FDP).We derive the convergence rate of the proposed estimator and numerically compare the false discovery rate (FDR) and the true positive rate (TPR) of our method to many existing procedures, including those from Benjamini and Hochberg (1995), Efron (2004), and Wang and Fan (2017).We demonstrate our method through simulation studies and analysis of protein phosphorylation levels for serous ovarian adenocarcinoma samples.