Estimating the marginal null distribution via empirical Bayes produces refined p-values that restore power in one-sided multiple testing when conventional p-values are conservative due to negative null means.
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Multiple Testing of One-Sided Hypotheses with Conservative $p$-values
Estimating the marginal null distribution via empirical Bayes produces refined p-values that restore power in one-sided multiple testing when conventional p-values are conservative due to negative null means.