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.
Bandwidth, Infill asymptotics, Intensity function, Kernel estimator, Mean squared error, Point process
Methodology and Computing in Applied Probability

van Lieshout, M.N.M. (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