Z-value Directional False Discovery Rate Control with Data Masking
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We revisit the fundamental "normal-means" problem, where independent normal test statistics z_i ∼ N(μ_i, 1), i = 1, …, m, also known as "z-values", are observed for the mean effects μ_1, …, μ_m. While there is extensive literature on testing the point null hypotheses μ_i = 0 with false discovery rate control, the problem of declaring whether μ_i is positive or negative with directional false discovery rate (dFDR) control has been much underserved. Leveraging the recently invented "data masking" technique, we propose a computationally efficient testing algorithm, called ZDIRECT, that seeks to mimic the optimal discovery procedure motivated by a Bayesian perspective yet provides exact dFDR control under minimal pure frequentist assumptions. In our simulation studies, ZDIRECT has demonstrated an apparent power advantage over the directional Benjamini and Hochberg procedure, which, to the best of our knowledge, is the only other existing procedure that offers dFDR control for the normal-means problem.
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