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.
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Acknowledgments
The author would like to thank sincerely Michaela Prokešová for discussing the initial idea of this paper, Frédéric Lavancier for discussions on an earlier version of the manuscript and Jérôme Lelong for a careful reading. The author is very grateful to the associate editor and the referee in particular for pointing out interesting references, which enriched the simulation study. The research of the author is partially funded by Persyval-lab EA Oculo-Nimbus.
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Coeurjolly, JF. Median-based estimation of the intensity of a spatial point process. Ann Inst Stat Math 69, 303–331 (2017). https://doi.org/10.1007/s10463-015-0536-7
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DOI: https://doi.org/10.1007/s10463-015-0536-7