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Abstract:
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Image data as high-dimensional and complex measurements are known to be observed with errors that come from multiple sources. Such errors include both random noises and systematic errors that are spatially correlated. With relatively small sample size in most of the study and limited availability of replicates for each participant, statistical inference made based on imaging data with errors might induce bias. We extend the shrinkage estimation idea in imaging data that was previously proposed to scalar-on-function regression setting and generalize the classical regression calibration in scalar data to functional regression. By shrinking the individual image towards population average image on the levels of individual voxels, local neighbors and the whole brain, we are able to calibrate the spatially dependent regression coefficient via the estimated attenuation ratio. Simulation studies show that the proposed approaches are able to reduce the data noise via borrowing information from the population image, and preserve the subject-specific image features. Results from application in improving understanding of resting state functional connectivity will be shown.
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