Dual Control of Testing Errors in High-Dimensional Data Analysis
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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 level. We propose a Dual Control of Errors (DCOE) method that regulates not only false positive but also false negative errors in measures that are highly relevant to high-dimensional data analysis. DCOE is developed under general covariance dependence with a new calibration procedure to measure the dependence effect. We specify how dependence co-acts with signal sparsity to determine the difficulty level of the dual control task and prove that DCOE is effective in retaining true signals that are not identifiable at individual level. Simulation studies are conducted to compare the new method with existing methods that focus on only one type of error. DCOE is shown to be more powerful than FDR methods and less aggressive than existing false negative control methods. DCOE is applied to a fMRI dataset to identify 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.
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