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Estimation of the intensity of a Poisson point process by means of nearest neighbor distances

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  • V. Granville

Abstract

A new unbiased consistent asymptotically normal estimator Uk of the intensity λ of a stationary multivariate Poisson point process is exhibited. This estimate is based on a combination of the j‐th nearest neighbor (possibly non Euclidean) distances (j=1, ..., k) to a single fixed site x. A simple closed form containing logarithmic terms is obtained for E(Ulk)(0

Suggested Citation

  • V. Granville, 1998. "Estimation of the intensity of a Poisson point process by means of nearest neighbor distances," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 52(1), pages 112-124, March.
    • Handle: RePEc:bla:stanee:v:52:y:1998:i:1:p:112-124
    DOI: 10.1111/1467-9574.00071
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    Cited by:

    1. 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.
    2. Marie-Colette N. M. Lieshout, 2012. "On Estimation of the Intensity Function of a Point Process," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 567-578, September.

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