intensity_bandwidth_profile: Find the optimal smoothing for intensity estimation kernel...

In antiphon/Kdirectional: Analysis of anisotropy in point patterns using second order statistics

Find the optimal smoothing for intensity estimation kernel width

Description

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.

Details

Optimize bandwidth $h$ using the Cronie & van Lieshout method [1]. In short, optimise the loss function

∑ 1/\hatλ_h(x_i) - |W|)^2

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].

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.

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

antiphon/Kdirectional documentation built on Feb. 13, 2023, 6:26 a.m.