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Abstract:
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Functional data analysis has become a powerful tool for conducting statistical analysis for complex objects. Among these data objects, images obtained using medical imaging technologies have been attracting researchers' attention. Examples are functional magnetic resonance imaging (fMRI) and positron emission tomography (PET), which provide a very detailed characterization of brain activity. In general, complex objects are often collected on a domain with an irregular boundary. To address this problem, we model the complex data objects as functional data and propose a multivariate spline method for estimating the mean functions of 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 the uncertainty of the estimation.
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