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 Rd are superposed. When the same bandwidth is used in all d dimensions, we show that an optimal bandwidth exists and is of the order nāˆ’1/(d+4) under appropriate smoothness conditions on the true intensity function.
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Methodology and Computing in Applied Probability

van Lieshout, M.-C. (2020). Infill asymptotics and bandwidth selection for kernel estimators of spatial intensity functions. Methodology and Computing in Applied Probability, 22(3), 995ā€“1008. doi:10.1007/s11009-019-09749-x