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Nonparametric estimation of the intensity function of a spatial point process on a Riemannian manifold

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  • S Ward
  • H S Battey
  • E A K Cohen

Abstract

SummaryThis paper is concerned with nonparametric estimation of the intensity function of a point process on a Riemannian manifold. It provides a first-order asymptotic analysis of the proposed kernel estimator for Poisson processes, supplemented by empirical work to probe the behaviour in finite samples and under other generative regimes. The investigation highlights the scope for finite-sample improvements by allowing the bandwidth to adapt to local curvature.

Suggested Citation

  • 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.
    • Handle: RePEc:oup:biomet:v:110:y:2023:i:4:p:1009-1021.
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    References listed on IDEAS

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    1. Pelletier, Bruno, 2005. "Kernel density estimation on Riemannian manifolds," Statistics & Probability Letters, Elsevier, vol. 73(3), pages 297-304, July.
    2. 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.
    3. 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.
    4. Peter Diggle, 1985. "A Kernel Method for Smoothing Point Process Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 34(2), pages 138-147, June.
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