Kernel smoothing of spatial point data can often be improved using an adaptive, spatially varying bandwidth instead of a fixed bandwidth. However, computation with a varying bandwidth is much more demanding, especially when edge correction and bandwidth selection are involved. This paper proposes several new computational methods for adaptive kernel estimation from spatial point pattern data. A key idea is that a variable-bandwidth kernel estimator for d-dimensional spatial data can be represented as a slice of a fixed-bandwidth kernel estimator in (d+1)
Kernel smoothing is a versatile tool for analysing spatial data: it is used to estimate probability density, point process intensity, relative risk, spatial regression functions and other quantities. Efficient algorithms for kernel smoothing are vital and must continually be improved in order to handle larger and more complex datasets.
