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Nonparametric density estimation over complicated domains

Author

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  • Federico Ferraccioli
  • Eleonora Arnone
  • Livio Finos
  • James O. Ramsay
  • Laura M. Sangalli

Abstract

We propose a nonparametric method for density estimation over (possibly complicated) spatial domains. The method combines a likelihood approach with a regularization based on a differential operator. We demonstrate the good inferential properties of the method. Moreover, we develop an estimation procedure based on advanced numerical techniques, and in particular making use of finite elements. This ensures high computational efficiency and enables great flexibility. The proposed method efficiently deals with data scattered over regions having complicated shapes, featuring complex boundaries, sharp concavities or holes. Moreover, it captures very well complicated signals having multiple modes with different directions and intensities of anisotropy. We show the comparative advantages of the proposed approach over state of the art methods, in simulation studies and in an application to the study of criminality in the city of Portland, Oregon.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssb:v:83:y:2021:i:2:p:346-368
    DOI: 10.1111/rssb.12415
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    References listed on IDEAS

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    1. D. Simpson & J. B. Illian & F. Lindgren & S. H. Sørbye & H. Rue, 2016. "Going off grid: computationally efficient inference for log-Gaussian Cox processes," Biometrika, Biometrika Trust, vol. 103(1), pages 49-70.
    2. Kim, Yoon Tae & Park, Hyun Suk, 2013. "Geometric structures arising from kernel density estimation on Riemannian manifolds," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 112-126.
    3. Suman Rakshit & Tilman Davies & M. Mehdi Moradi & Greg McSwiggan & Gopalan Nair & Jorge Mateu & Adrian Baddeley, 2019. "Fast Kernel Smoothing of Point Patterns on a Large Network using Two‐dimensional Convolution," International Statistical Review, International Statistical Institute, vol. 87(3), pages 531-556, December.
    4. B. Ettinger & S. Perotto & L. M. Sangalli, 2016. "Spatial regression models over two-dimensional manifolds," Biometrika, Biometrika Trust, vol. 103(1), pages 71-88.
    5. Greg McSwiggan & Adrian Baddeley & Gopalan Nair, 2017. "Kernel Density Estimation on a Linear Network," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 324-345, June.
    6. Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392, April.
    7. Berry, Tyrus & Sauer, Timothy, 2017. "Density estimation on manifolds with boundary," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 1-17.
    8. 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.
    9. Gu, Chong, 2014. "Smoothing Spline ANOVA Models: R Package gss," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 58(i05).
    10. 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.
    11. Finn Lindgren & Håvard Rue & Johan Lindström, 2011. "An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(4), pages 423-498, September.
    12. 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.
    13. Isabel Fuentes-Santos & Wenceslao González-Manteiga & Jorge Mateu, 2016. "Consistent Smooth Bootstrap Kernel Intensity Estimation for Inhomogeneous Spatial Poisson Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 416-435, June.
    14. 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.
    15. 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.
    16. 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.
    17. Lindgren, Finn & Rue, Håvard, 2015. "Bayesian Spatial Modelling with R-INLA," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i19).
    18. Yongtao Guan & Ye Shen, 2010. "A weighted estimating equation approach for inhomogeneous spatial point processes," Biometrika, Biometrika Trust, vol. 97(4), pages 867-880.
    19. Carando, Daniel & Fraiman, Ricardo & Groisman, Pablo, 2009. "Nonparametric likelihood based estimation for a multivariate Lipschitz density," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 981-992, May.
    20. Rasmus Waagepetersen & Yongtao Guan, 2009. "Two‐step estimation for inhomogeneous spatial point processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 685-702, June.
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    Cited by:

    1. Laura M. Sangalli, 2021. "Spatial Regression With Partial Differential Equation Regularisation," International Statistical Review, International Statistical Institute, vol. 89(3), pages 505-531, December.
    2. 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).
    3. Alexander Gleim & Nazarii Salish, 2022. "Forecasting Environmental Data: An example to ground-level ozone concentration surfaces," Papers 2202.03332, arXiv.org.

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