High-Dimensional Inference for Unidentifiable Signals with False Negative Control

False negative errors are of major concern in applications where missing a high proportion of true signals may cause serious consequences. False negative control, however, raises a bottleneck challenge in high-dimensional inference when signals are not identifiable at individual levels. We develop a new analytic framework to regulate false negative errors under measures tailored towards modern applications with high-dimensional data. A new method is proposed in realistic settings with arbitrary covariance dependence between variables. We explicate the joint effects of covariance dependence and signal sparsity on the new method and interpret the results using a phase diagram. It shows that signals that are not individually identifiable can be effectively retained by the proposed method without incurring excessive false positives. Simulation studies are conducted to compare the new method with several existing methods. The new method outperforms the others in adapting to a user-specified false negative control level. We apply the new method to analyze an fMRI dataset to locate voxels that are functionally relevant to saccadic eye movements. The new method exhibits a nice balance in retaining signal voxels and avoiding excessive noise voxels.