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Abstract:
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Weak signal inference emerges in modern applications where important signals may not be identifiable at individual levels in large-scale complex datasets, such as fMRI data. We address the challenge from the perspective of false negative control and develop a new method to efficiently regulate the false negative proportion at a user-specified level. The new method is developed in realistic settings with arbitrary covariance dependence between variables. We calibrate the overall dependence through a parameter whose scale is compatible with the existing phase diagram in high-dimensional sparse inference. Utilizing the new calibration, we asymptotically explicate the joint effect of covariance dependence, signal sparsity, and signal intensity on the proposed method. The theoretical results are interpreted through a new phase diagram, where it shows that the proposed method can efficiently retain a high proportion of signals even when they are not separable from noise. The performance of the proposed method in finite sample and saccadic eye movements datasets is compared to several existing methods in simulation studies.
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