Department of Statistics
Iowa State University
Estimation and Inference for Image-on-Scalar Regression with Application to Imaging Genetics Studies
Motivated by recent work of analyzing data in the imaging genetics studies, we consider a class of linear functional regression models for imaging responses and scalar predictors. To handle the irregular domain of the region of interest on the images and other characteristics of images, we propose to use flexible bivariate splines over triangulations to achieve the low-dimensional representation of functional data. The proposed estimators of the coefficient functions are proved to be root-n consistent and asymptotically normal under some regularity conditions. We also provide a computationally efficient estimator of the covariance function and derive its uniform consistency. Asymptotic confidence intervals and data-driven confidence corridors for the coefficient maps are constructed. Our method can simultaneously estimate and make inferences of the coefficient functions while incorporating the spatial heterogeneity and spatial smoothness. Highly efficient and scalable estimation algorithm is developed for the joint analysis of both high-dimensional imaging phenotypes and high-dimensional genetic data. Monte Carlo simulation studies are conducted to examine the finite-sample performance of the proposed method. The proposed method is applied to the spatially normalized Positron Emission Tomography (PET) data of Alzheimer's Disease Neuroimaging Initiative (ADNI).
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