Find the optimal smoothing for intensity estimation kernel width

Usage

intensity_bandwidth_profile(x, bw_vector, kernel = "gaussian", ...)

Arguments

x: point pattern
bw_vector: Vector of bandwidth values to optimize over
kernel: Either 'gaussian' or 'epanenchnikov'
...: ignored.

Value

list with elements:

* opt: the optimal bandwidth, given the inputs

* iopt: index of optimal bandwidth in input vector

* loss: the squared loss function (given above)

* statistic: the statistic which root is to be found

* area: window area |W| used for optimisation.

Details

Optimize bandwidth $h$ using the Cronie & van Lieshout method [1]. In short, optimise the loss function $$latex$$ with a kernel intensity estimator. See Reference for the paper.

Note: The optimisation is done without border correction and without leave-one-out, as suggested in [1].

References

1. Cronie O, van Lieshout MNM. Bandwidth selection for kernel estimators of the spatial intensity function. 2016;1-20. Available from: http://arxiv.org/abs/1611.10221