Abstract
We investigate the asymptotic mean squared error of kernel estimators of the intensity function of a spatial point process. We derive expansions for the bias and variance in the scenario that n independent copies of a point process in \(\mathbb {R}^{d}\) are superposed. When the same bandwidth is used in all d dimensions, we show that an optimal bandwidth exists and is of the order n− 1/(d+ 4) under appropriate smoothness conditions on the true intensity function.
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This research was partially supported by The Netherlands Organisation for Scientific Research NWO (project DEEP.NL.2018.033).
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van Lieshout, M.N.M. Infill Asymptotics and Bandwidth Selection for Kernel Estimators of Spatial Intensity Functions. Methodol Comput Appl Probab 22, 995–1008 (2020). https://doi.org/10.1007/s11009-019-09749-x
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DOI: https://doi.org/10.1007/s11009-019-09749-x