Bandwidth Selection Based on Window Geometry
Select a smoothing bandwidth for smoothing a point pattern, based only on the geometry of the spatial window. The bandwidth is a specified quantile of the distance between two independent random points in the window.
bw.frac(X, ..., f=1/4)
This function selects an appropriate bandwidth sigma
for the kernel estimator of point process intensity
computed by density.ppp.
The bandwidth σ is computed as a quantile of the distance between two independent random points in the window. The default is the lower quartile of this distribution.
If F(r) is the cumulative distribution function of the distance between two independent random points uniformly distributed in the window, then the value returned is the quantile with probability f. That is, the bandwidth is the value r such that F(r) = f.
The cumulative distribution function F(r) is
computed using distcdf. We then
we compute the smallest number r
such that F(r) >= f.
A numerical value giving the selected bandwidth.
The result also belongs to the class "bw.frac"
which can be plotted to show the cumulative distribution function
and the selected quantile.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.
For estimating point process intensity, see
density.ppp,
bw.diggle,
bw.ppl,
bw.scott,
bw.CvL.
For other smoothing purposes, see
bw.stoyan,
bw.smoothppp,
bw.relrisk.
h <- bw.frac(letterR) h plot(h, main="bw.frac(letterR)")
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