spatstat.explore (version 3.5-3)

bw.CvL: Cronie and van Lieshout's Criterion for Bandwidth Selection for Kernel Density

Description

Uses Cronie and van Lieshout's criterion based on Cambell's formula to select a smoothing bandwidth for the kernel estimation of point process intensity.

Usage

bw.CvL(X, ..., srange = NULL, ns = 16, sigma = NULL, warn=TRUE)

Value

A single numerical value giving the selected bandwidth. The result also belongs to the class "bw.optim"

(see bw.optim.object) which can be plotted to show the bandwidth selection criterion as a function of sigma.

Details

This function selects an appropriate bandwidth sigma for the kernel estimator of point process intensity computed by density.ppp.

The bandwidth \(\sigma\) is chosen to minimise the discrepancy between the area of the observation window and the sum of reciprocal estimated intensity values at the points of the point process $$ \mbox{CvL}(\sigma) = (|W| - \sum_i 1/\hat\lambda(x_i))^2 $$ where the sum is taken over all the data points \(x_i\), and where \(\hat\lambda(x_i)\) is the kernel-smoothing estimate of the intensity at \(x_i\) with smoothing bandwidth \(\sigma\).

The value of \(\mbox{CvL}(\sigma)\) is computed directly, using density.ppp, for ns different values of \(\sigma\) between srange[1] and srange[2].

References

Cronie, O and Van Lieshout, M N M (2018) A non-model-based approach to bandwidth selection for kernel estimators of spatial intensity functions, Biometrika, 105, 455-462.

See Also

density.ppp, bw.optim.object.

Alternative methods: bw.diggle, bw.scott, bw.ppl, bw.frac.

For adaptive smoothing bandwidths, use bw.CvL.adaptive.

Examples

  if(interactive()) {
    b <- bw.CvL(redwood)
    b
    plot(b, main="Cronie and van Lieshout bandwidth criterion for redwoods")
    plot(density(redwood, b))
    plot(density(redwood, bw.CvL))
  }
  # \testonly{
    b <- bw.CvL(redwood, srange=c(0.03, 0.07), ns=2)
  # }