Abstract:
Motivated by recent work on studying massive imaging data in various neuroimaging studies, our group proposes several classes of spatial regression models including spatially varying coefficient models, spatial predictive Gaussian process models, tensor regression models, and Cox functional linear regression models for the joint analysis of large neuroimaging data and clinical and behavioral data. Our statistical models explicitly account for several stylized features of neuroimaging data: the presence of multiple piecewise smooth regions with unknown edges and jumps and substantial spatial correlations. We develop some fast estimation procedures to simultaneously estimate the varying coefficient functions and the spatial correlations. We systematically investigate the asymptotic properties (e.g., consistency and asymptotic normality) of the multi-scale adaptive parameter estimates. Our Monte Carlo simulation and real data analysis have confirmed the excellent performance of our models in different applications.
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