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Title: Functional covariance estimation for partially observed functional data Authors:  Uche Mbaka - University College Dublin (Ireland) [presenting]
Michelle Carey - Univerity College Dublin (Ireland)
Abstract: Most approaches for reconstructing curves from partially observed functional samples depend on estimating the covariance surface. We propose an approach for estimating the covariance surface from sparse and fragmented functional observations using a finite element method called finite element sigma (FE-Sigma). When applied to densely observed functional data, the finite element sigma produces a covariance surface with the desirable property of being positive definite, which leads to an accurate estimation of the inverse covariance surface (i.e., the precision surface). By including this improved estimate of the covariance surface in the principal analysis by conditional expectation (PACE) approach, we can obtain improved estimates of the principal functional components and use these functions to estimate full curves. We compare the results of curve estimation accuracy using a simulated dataset and apply the new approach to a real dataset (somatic cell scores of dairy cows from selected Irish farms).