Marie-Colette van Lieshout (CWI and University of Twente): Bandwidth selection for kernel estimators of spatial intensity functions
The analysis of a spatial point pattern usually involves estimating the intensity function, that is, the likelihood of finding a point as a function of location. Sometimes the scientific context suggests a parametric form for the intensity function, perhaps in terms of covariate information. More often, non-parametric estimation is called for. In this case, kernel estimators can be used. They involve one crucial parameter: the bandwidth.
In this talk, I will first describe various widely used bandwidth selection methods and compare their efficacy on simulations and actual data on earthquakes in the Groningen gas field.
Next, I will discuss asymptotic expansions of the mean squared error when independent copies of the point process are superposed. I will show that the optimal bandwidth is of the order $n^{-1/(d+4)}$ under appropriate smoothness conditions on the kernel and true intensity function. Moreover, the Abramson principle can be applied to define adaptive kernel estimators. The optimal adaptive bandwidth turns out to be of the order $n^{-1/(d+8)}$ under appropriate smoothness conditions.
This talk is partially based on joint work with Zhuldyzay Baki and Ottmar Cronie.