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Title: Statistical inference for mean functions of 3D functional objects Authors:  Yueying Wang - Iowa State University (United States)
Brandon Klinedinst - Iowa State University (United States)
Guannan Wang - College of William \& Mary (United States)
Auriel Willette - Iowa State University (United States)
Lily Wang - George Mason University (United States) [presenting]
Abstract: Functional data analysis has become a powerful tool for the statistical analysis of complex objects, such as curves, images, shapes, and manifold-valued data. Among these data objects, 2D or 3D images obtained using medical imaging technologies have been attracting researchers' attention. In general, 3D complex objects are usually collected within the irregular boundary, whereas the majority of existing statistical methods have been focused 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 a two-sample case is discussed together with numerical experiments and a real-data application using Alzheimer's Disease Neuroimaging Initiative database.