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Finite area smoothing with generalized distance splines

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DOI

Abstract

Most conventional spatial smoothers smooth with respect to the Euclidean distance between observations, even though this distance may not be a meaningful measure of spatial proximity, especially when boundary features are present. When domains have complicated boundaries leakage (the inappropriate linking of parts of the domain which are separated by physical barriers) can occur. To overcome this problem, we develop a method of smoothing with respect to generalized distances, such as within domain distances. We obtain the generalized distances between our points and then use multidimensional scaling to find a configuration of our observations in a Euclidean space of 2 or more dimensions, such that the Euclidian distances between points in that space closely approximate the generalized distances between the points. Smoothing is performed over this new point configuration, using a conventional smoother. To mitigate the problems associated with smoothing in high dimensions we use a generalization of thin plate spline smoothers proposed by Duchon (Constructive theory of functions of several variables, pp 85-100, 1977). This general method for smoothing with respect to generalized distances improves on the performance of previous within-domain distance spatial smoothers, and often provides a more natural model than the soap film approach of Wood et al. (J R Stat Soc Ser B Stat Methodol 70(5):931-955, 2008). The smoothers are of the linear basis with quadratic penalty type easily incorporated into a range of statistical models.
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Original languageEnglish
Pages (from-to)715-731
Number of pages17
JournalEnvironmental and Ecological Statistics
Volume21
Issue number4
Early online date26 Feb 2014
DOIs
StatePublished - 2014

    Research areas

  • Finite area smoothing, Generalized additive model, Multidimensional scaling, Spatial modeling, Splines

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