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Abstract:
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In this article, we propose a generalized multiple testing procedure, which is a weighted version of the well-known Benjamini-Hochberg (BH) procedure. The rigorous weighing scheme used by our method, enables it to encode structural information from simultaneous multi-way classification as well as hierarchical partitioning of hypotheses into groups, with provisions to accommodate overlapping groups. The method is proven to control the False Discovery Rate (FDR) when the p-values involved are Positively Regression Dependent on the Subset (PRDS) of null p-values and is shown to be more powerful than existing comparable multiple testing procedures. The corresponding data-adaptive version of the method is powerful and controls FDR under the assumption that the p-values involved are independent. We apply this procedure to an EEG dataset to exploit its complex spatio-temporal structure and analyze the impact of alcoholism on the human brain.
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