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Non-parametric adaptive bandwidth selection for kernel estimators of spatial intensity functions

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  • M. N. M. Lieshout

    (CWI
    University of Twente)

Abstract

We introduce a new fully non-parametric two-step adaptive bandwidth selection method for kernel estimators of spatial point process intensity functions based on the Campbell–Mecke formula and Abramson’s square root law. We present a simulation study to assess its performance relative to other adaptive and global bandwidth selectors, investigate the influence of the pilot estimator and apply the technique to two data sets: A pattern of trees and an earthquake catalogue.

Suggested Citation

  • M. N. M. Lieshout, 2024. "Non-parametric adaptive bandwidth selection for kernel estimators of spatial intensity functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(2), pages 313-331, April.
    • Handle: RePEc:spr:aistmt:v:76:y:2024:i:2:d:10.1007_s10463-023-00890-6
    DOI: 10.1007/s10463-023-00890-6
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    References listed on IDEAS

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    1. C. D. Barr & F. P. Schoenberg, 2010. "On the Voronoi estimator for the intensity of an inhomogeneous planar Poisson process," Biometrika, Biometrika Trust, vol. 97(4), pages 977-984.
    2. 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.
    3. Davies, Tilman M. & Flynn, Claire R. & Hazelton, Martin L., 2018. "On the utility of asymptotic bandwidth selectors for spatially adaptive kernel density estimation," Statistics & Probability Letters, Elsevier, vol. 138(C), pages 75-81.
    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.
    5. Brooks, Maria Mori & Marron, J. Stephen, 1991. "Asymptotic optimality of the least-squares cross-validation bandwidth for kernel estimates of intensity functions," Stochastic Processes and their Applications, Elsevier, vol. 38(1), pages 157-165, June.
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