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Abstract:
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Existing approaches for multivariate functional principal component analysis are restricted to data on a single interval. The presented approach focuses on multivariate functional data on different domains that may differ in dimension, e.g. functions and images. The theoretical basis for multivariate functional principal component analysis is given in terms of a Karhunen-Loeve Theorem. For the practically relevant case of a finite Karhunen-Loeve representation, a relationship between univariate and multivariate functional principal component analysis is established. This offers a simple estimation strategy to calculate multivariate functional principal components and scores based on their univariate counterparts. The approach can be extended to finite expansions in general, not necessarily orthonormal bases and is also applicable for sparse data or data with measurement error. A flexible software implementation is available. As motivating application we present the results for a neuroimaging study, where the goal is to explore how longitudinal trajectories of a neuropsychological test score covary with FDG-PET brain scans at baseline.
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