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

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 with the standard one counting the mean number of points per unit volume. The empirical study verifies the asymptotic properties established and shows that the median-based estimator is more robust to outliers than the standard estimator.
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https://hal.archives-ouvertes.fr/hal-01071605
Contributor : Jean-François Coeurjolly <>
Submitted on : Sunday, May 24, 2015 - 2:47:41 PM
Last modification on : Monday, December 14, 2020 - 3:40:12 PM
Long-term archiving on: : Thursday, April 20, 2017 - 7:40:41 AM

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Jean-François Coeurjolly. Median-based estimation of the intensity of a spatial point process. Annals of the Institute of Statistical Mathematics, Springer Verlag, 2017, 69 (2), pp.303-331. ⟨10.1007/s10463-015-0536-7⟩. ⟨hal-01071605v2⟩

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