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Modeling spatially dependent functional data via regression with differential regularization

Author

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  • Arnone, Eleonora
  • Azzimonti, Laura
  • Nobile, Fabio
  • Sangalli, Laura M.

Abstract

We propose a method for modeling spatially dependent functional data, based on regression with differential regularization. The regularizing term enables to include problem-specific information about the spatio-temporal variation of the phenomenon under study, formalized in terms of a time-dependent partial differential equation. The method is implemented using a discretization based on finite elements in space and finite differences in time. This non-tensor product basis allows to handle efficiently data distributed over complex domains and where the shape of the domain influences the phenomenon’s behavior. Moreover, the method can comply with specific conditions at the boundary of the domain of interest. Simulation studies compare the proposed model to available techniques for spatio-temporal data. The method is also illustrated via an application to the study of blood-flow velocity field in a carotid artery affected by atherosclerosis, starting from echo-color doppler and magnetic resonance imaging data.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:170:y:2019:i:c:p:275-295
    DOI: 10.1016/j.jmva.2018.09.006
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    References listed on IDEAS

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    1. Menafoglio, Alessandra & Secchi, Piercesare, 2017. "Statistical analysis of complex and spatially dependent data: A review of Object Oriented Spatial Statistics," European Journal of Operational Research, Elsevier, vol. 258(2), pages 401-410.
    2. Jiguo Cao & Gregor F. Fussmann & James O. Ramsay, 2008. "Estimating a Predator‐Prey Dynamical Model with the Parameter Cascades Method," Biometrics, The International Biometric Society, vol. 64(3), pages 959-967, September.
    3. 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.
    4. Laura Azzimonti & Laura M. Sangalli & Piercesare Secchi & Maurizio Domanin & Fabio Nobile, 2015. "Blood Flow Velocity Field Estimation Via Spatial Regression With PDE Penalization," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1057-1071, September.
    5. B. Ettinger & S. Perotto & L. M. Sangalli, 2016. "Spatial regression models over two-dimensional manifolds," Biometrika, Biometrika Trust, vol. 103(1), pages 71-88.
    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. Xiaolei Xun & Jiguo Cao & Bani Mallick & Arnab Maity & Raymond J. Carroll, 2013. "Parameter Estimation of Partial Differential Equation Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 1009-1020, September.
    8. 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.
    9. Giampiero Marra & David L. Miller & Luca Zanin, 2012. "Modelling the spatiotemporal distribution of the incidence of resident foreign population," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 66(2), pages 133-160, May.
    10. Nerini, David & Monestiez, Pascal & Manté, Claude, 2010. "Cokriging for spatial functional data," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 409-418, February.
    11. J. O. Ramsay & G. Hooker & D. Campbell & J. Cao, 2007. "Parameter estimation for differential equations: a generalized smoothing approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 741-796, November.
    12. Nicole H. Augustin & Verena M. Trenkel & Simon N. Wood & Pascal Lorance, 2013. "Space‐time modelling of blue ling for fisheries stock management," Environmetrics, John Wiley & Sons, Ltd., vol. 24(2), pages 109-119, March.
    13. Laura M. Sangalli & James O. Ramsay & Timothy O. Ramsay, 2013. "Spatial spline regression models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 681-703, September.
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    Citations

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    Cited by:

    1. Římalová, Veronika & Fišerová, Eva & Menafoglio, Alessandra & Pini, Alessia, 2022. "Inference for spatial regression models with functional response using a permutational approach," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    2. Federico Ferraccioli & Eleonora Arnone & Livio Finos & James O. Ramsay & Laura M. Sangalli, 2021. "Nonparametric density estimation over complicated domains," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(2), pages 346-368, April.
    3. Arnone, Eleonora & Ferraccioli, Federico & Pigolotti, Clara & Sangalli, Laura M., 2022. "A roughness penalty approach to estimate densities over two-dimensional manifolds," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    4. Aneiros, Germán & Cao, Ricardo & Fraiman, Ricardo & Genest, Christian & Vieu, Philippe, 2019. "Recent advances in functional data analysis and high-dimensional statistics," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 3-9.
    5. Ferraccioli, Federico & Sangalli, Laura M. & Finos, Livio, 2022. "Some first inferential tools for spatial regression with differential regularization," Journal of Multivariate Analysis, Elsevier, vol. 189(C).

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