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Finite area smoothing with generalized distance splines

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Finite area smoothing with generalized distance splines. / Miller, D.L.; Wood, S.N.

In: Environmental and Ecological Statistics, Vol. 21, No. 4, 2014, p. 715-731.

Research output: Contribution to journalArticle

Harvard

Miller, DL & Wood, SN 2014, 'Finite area smoothing with generalized distance splines' Environmental and Ecological Statistics, vol. 21, no. 4, pp. 715-731. https://doi.org/10.1007/s10651-014-0277-4

APA

Miller, D. L., & Wood, S. N. (2014). Finite area smoothing with generalized distance splines. Environmental and Ecological Statistics, 21(4), 715-731. https://doi.org/10.1007/s10651-014-0277-4

Vancouver

Miller DL, Wood SN. Finite area smoothing with generalized distance splines. Environmental and Ecological Statistics. 2014;21(4):715-731. https://doi.org/10.1007/s10651-014-0277-4

Author

Miller, D.L. ; Wood, S.N. / Finite area smoothing with generalized distance splines. In: Environmental and Ecological Statistics. 2014 ; Vol. 21, No. 4. pp. 715-731.

Bibtex - Download

@article{1709f2605315441f9fd64a12f6b853a6,
title = "Finite area smoothing with generalized distance splines",
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.",
keywords = "Finite area smoothing, Generalized additive model, Multidimensional scaling, Spatial modeling, Splines",
author = "D.L. Miller and S.N. Wood",
year = "2014",
doi = "10.1007/s10651-014-0277-4",
language = "English",
volume = "21",
pages = "715--731",
journal = "Environmental and Ecological Statistics",
issn = "1352-8505",
publisher = "Springer",
number = "4",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Finite area smoothing with generalized distance splines

AU - Miller, D.L.

AU - Wood, S.N.

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - Finite area smoothing

KW - Generalized additive model

KW - Multidimensional scaling

KW - Spatial modeling

KW - Splines

UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84894260707&partnerID=8YFLogxK

U2 - 10.1007/s10651-014-0277-4

DO - 10.1007/s10651-014-0277-4

M3 - Article

VL - 21

SP - 715

EP - 731

JO - Environmental and Ecological Statistics

T2 - Environmental and Ecological Statistics

JF - Environmental and Ecological Statistics

SN - 1352-8505

IS - 4

ER -

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