Speaker: Yueying Wang
Abstract: Functional data analysis has become a powerful tool for conducting statistical analysis for complex objects, such as curves, images, shapes and manifold-valued data. Among these data objects, 2D or 3D images obtained using medical imaging technologies emerging recently have been attracting researchers' attention. Examples are functional magnetic resonance imaging (fMRI) and positron emission tomography (PET), which provides very detailed characterization of brain activity. In general, 3D complex objects are usually collected within the irregular boundary, whereas the majority of existing statistical methods have been focusing on a regular domain. To address this problem, we model the complex data objects as functional data and propose trivariate spline smoothing based on tetrahedralizations for estimating the mean functions of 3D functional objects. The asymptotic properties of the proposed estimator are systematically investigated where consistency and asymptotic normality are established. We also provide a computationally efficient estimation procedure for covariance function and corresponding eigenvalue and eigenfunctions and derive uniform consistency. Motivated by the need for statistical inference for complex functional objects, we then present a novel approach for constructing simultaneous confidence corridors to quantify estimation uncertainty. Extension of the procedure to the two-sample case is discussed together with numerical experiments and a real-data application using Alzheimer's Disease Neuroimaging Initiative database.