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Low-Rank Smoothing Splines on Complicated Domains



Summary Smoothing over a domain with irregular boundaries or interior gaps and holes is addressed. Consider the problem of estimating mercury in sediment concentrations in the estuarine waters in New Hampshire. A modified version of low-rank thin plate splines (LTPS) is introduced where the geodesic distance is applied to evaluate dissimilarity of any two data observations: loosely speaking, distances between locations are not measured as the crow flies, but as the fish swims. The method is compared with competing smoothing techniques, LTPS, and finite element L-splines.