Wavelet-based Benjamini-Hochberg procedures for multiple testing under dependence

Multiple comparisons methodology has experienced a resurgence of interest due to the increase in high-dimensional datasets generated from various biological, medical and scientific fields. An outstanding problem in this area is how to perform testing in the presence of dependence between the p-values. We propose a novel approach to this problem based on a spacings-based representation of the Benjamini-Hochberg procedure. The representation leads to a new application of the wavelet transform to effectively decorrelate p-values. Theoretical justification for the procedure is shown. The power gains of the proposed methodology relative to existing procedures is demonstrated using both simulated and real datasets.