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Median-based estimation of the intensity of a spatial point process

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  • Jean-François Coeurjolly

    (Univ. Grenoble Alpes)

Abstract

This paper is concerned with a robust estimator of the intensity of a stationary spatial point process. The estimator corresponds to the median of a jittered sample of the number of points, computed from a tessellation of the observation domain. We show that this median-based estimator satisfies a Bahadur representation from which we deduce its consistency and asymptotic normality under mild assumptions on the spatial point process. Through a simulation study, we compare the new estimator, in particular, with the standard one counting the mean number of points per unit volume. The empirical study confirms the asymptotic properties established in the theoretical part and shows that the median-based estimator is more robust to outliers than standard procedures.

Suggested Citation

  • Jean-François Coeurjolly, 2017. "Median-based estimation of the intensity of a spatial point process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(2), pages 303-331, April.
    • Handle: RePEc:spr:aistmt:v:69:y:2017:i:2:d:10.1007_s10463-015-0536-7
    DOI: 10.1007/s10463-015-0536-7
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    References listed on IDEAS

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    1. Jean-François Coeurjolly & Joëlle Rousseau Trépanier, 2020. "The median of a jittered Poisson distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(7), pages 837-851, October.

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