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A non-model-based approach to bandwidth selection for kernel estimators of spatial intensity functions

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  • O Cronie
  • M N M Van Lieshout

Abstract

SUMMARYWe propose a new bandwidth selection method for kernel estimators of spatial point process intensity functions. The method is based on an optimality criterion motivated by the Campbell formula applied to the reciprocal intensity function. The new method is fully nonparametric, does not require knowledge of higher-order moments, and is not restricted to a specific class of point process. Our approach is computationally straightforward and does not require numerical approximation of integrals.

Suggested Citation

  • O Cronie & M N M Van Lieshout, 2018. "A non-model-based approach to bandwidth selection for kernel estimators of spatial intensity functions," Biometrika, Biometrika Trust, vol. 105(2), pages 455-462.
    • Handle: RePEc:oup:biomet:v:105:y:2018:i:2:p:455-462.
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    File URL: http://hdl.handle.net/10.1093/biomet/asy001
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    Citations

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    Cited by:

    1. Kristian Bjørn Hessellund & Ganggang Xu & Yongtao Guan & Rasmus Waagepetersen, 2022. "Second‐order semi‐parametric inference for multivariate log Gaussian Cox processes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(1), pages 244-268, January.
    2. M. N. M. Lieshout, 2020. "Infill Asymptotics and Bandwidth Selection for Kernel Estimators of Spatial Intensity Functions," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 995-1008, September.
    3. S Ward & H S Battey & E A K Cohen, 2023. "Nonparametric estimation of the intensity function of a spatial point process on a Riemannian manifold," Biometrika, Biometrika Trust, vol. 110(4), pages 1009-1021.
    4. Mohammad Ghorbani & Ottmar Cronie & Jorge Mateu & Jun Yu, 2021. "Functional marked point processes: a natural structure to unify spatio-temporal frameworks and to analyse dependent functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 529-568, September.
    5. Borrajo, M.I. & González-Manteiga, W. & Martínez-Miranda, M.D., 2020. "Bootstrapping kernel intensity estimation for inhomogeneous point processes with spatial covariates," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    6. Amaya-Gómez, Rafael & Sánchez-Silva, Mauricio & Muñoz, Felipe & Schoefs, Franck & Bastidas-Arteaga, Emilio, 2024. "Spatial characterization and simulation of new defects in corroded pipeline based on In-Line Inspections," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    7. Michael Govorov & Giedrė Beconytė & Gennady Gienko, 2023. "Trivariate Kernel Density Estimation of Spatiotemporal Crime Events with Case Study for Lithuania," Sustainability, MDPI, vol. 15(11), pages 1-17, May.
    8. Ottmar Cronie & Mehdi Moradi & Christophe A N Biscio, 2024. "A cross-validation-based statistical theory for point processes," Biometrika, Biometrika Trust, vol. 111(2), pages 625-641.

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