题目：Conformalized Multiple Testing With Confident Directions

摘要：In large-scale studies, investigators often need to determine which effects are positive and which are negative. Reliable inference must account for errors in the reported directions, as well as differences in measurement precision across effects. We develop CORD, a directional multiple-testing procedure that learns the effect-size distribution to rank potential discoveries while accounting for unequal measurement precision. Comparisons with simulated zero-effect observations determine which discoveries to report. Effects without sufficient evidence receive no directional declaration. We control the directional false discovery rate: the expected proportion of reported discoveries that either have the wrong sign or correspond to zero effects. For independent normally distributed observations with known, possibly unequal variances, this control holds in finite samples even when the effect distribution is estimated inaccurately. A theoretical benchmark identifies how the effect distribution can be used to rank potential discoveries. Simulations show gains in correct directional discoveries, and a gene-expression analysis illustrates adaptation to different patterns of positive and negative effects.