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Soap film smoothing

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  • Simon N. Wood
  • Mark V. Bravington
  • Sharon L. Hedley

Abstract

Summary. Conventional smoothing methods sometimes perform badly when used to smooth data over complex domains, by smoothing inappropriately across boundary features, such as peninsulas. Solutions to this smoothing problem tend to be computationally complex, and not to provide model smooth functions which are appropriate for incorporating as components of other models, such as generalized additive models or mixed additive models. We propose a class of smoothers that are appropriate for smoothing over difficult regions of 2 which can be represented in terms of a low rank basis and one or two quadratic penalties. The key features of these smoothers are that they do not ‘smooth across’ boundary features, that their representation in terms of a basis and penalties allows straightforward incorporation as components of generalized additive models, mixed models and other non‐standard models, that smoothness selection for these model components is straightforward to accomplish in a computationally efficient manner via generalized cross‐validation, Akaike's information criterion or restricted maximum likelihood, for example, and that their low rank means that their use is computationally efficient.

Suggested Citation

  • Simon N. Wood & Mark V. Bravington & Sharon L. Hedley, 2008. "Soap film smoothing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 931-955, November.
  • Handle: RePEc:bla:jorssb:v:70:y:2008:i:5:p:931-955
    DOI: 10.1111/j.1467-9868.2008.00665.x
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    References listed on IDEAS

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    3. Simon N. Wood, 2004. "Stable and Efficient Multiple Smoothing Parameter Estimation for Generalized Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 673-686, January.
    4. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, October.
    5. Haonan Wang & M. Giovanna Ranalli, 2007. "Low-Rank Smoothing Splines on Complicated Domains," Biometrics, The International Biometric Society, vol. 63(1), pages 209-217, March.
    6. Tim Ramsay, 2002. "Spline smoothing over difficult regions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 307-319, May.
    7. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, October.
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    10. Lan Zhou & Huijun Pan, 2014. "Smoothing noisy data for irregular regions using penalized bivariate splines on triangulations," Computational Statistics, Springer, vol. 29(1), pages 263-281, February.
    11. Ji Yeh Choi & Heungsun Hwang & Marieke E. Timmerman, 2018. "Functional Parallel Factor Analysis for Functions of One- and Two-dimensional Arguments," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 1-20, March.
    12. Lee, Xing Ju & Hainy, Markus & McKeone, James P. & Drovandi, Christopher C. & Pettitt, Anthony N., 2018. "ABC model selection for spatial extremes models applied to South Australian maximum temperature data," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 128-144.
    13. W. Brunauer & S. Lang & P. Wechselberger & S. Bienert, 2010. "Additive Hedonic Regression Models with Spatial Scaling Factors: An Application for Rents in Vienna," The Journal of Real Estate Finance and Economics, Springer, vol. 41(4), pages 390-411, November.
    14. Wolfgang Brunauer & Stefan Lang & Peter Wechselberger & Sven Bienert, 2008. "Additive Hedonic Regression Models with Spatial Scaling Factors: An Application for Rents in Vienna," Working Papers 2008-17, Faculty of Economics and Statistics, Universität Innsbruck.
    15. Mu Niu & Pokman Cheung & Lizhen Lin & Zhenwen Dai & Neil Lawrence & David Dunson, 2019. "Intrinsic Gaussian processes on complex constrained domains," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(3), pages 603-627, July.
    16. Arnone, Eleonora & Azzimonti, Laura & Nobile, Fabio & Sangalli, Laura M., 2019. "Modeling spatially dependent functional data via regression with differential regularization," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 275-295.
    17. Williamson, Laura D. & Scott, Beth E. & Laxton, Megan & Illian, Janine B. & Todd, Victoria L.G. & Miller, Peter I. & Brookes, Kate L., 2022. "Comparing distribution of harbour porpoise using generalized additive models and hierarchical Bayesian models with integrated nested laplace approximation," Ecological Modelling, Elsevier, vol. 470(C).
    18. Bernardi, Mara S. & Carey, Michelle & Ramsay, James O. & Sangalli, Laura M., 2018. "Modeling spatial anisotropy via regression with partial differential regularization," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 15-30.
    19. Lin, Fangzheng & Tang, Yanlin & Zhu, Huichen & Zhu, Zhongyi, 2022. "Spatially clustered varying coefficient model," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
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    21. Arnab Bhattacharjee & Liqian Cai & Taps Maiti, 2013. "Functional regression over irregular domains," SEEC Discussion Papers 1301, Spatial Economics and Econometrics Centre, Heriot Watt University.

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