bw.CvL {spatstat.explore} | R Documentation |
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)
Arguments
X |
A point pattern (object of class |
... |
Ignored. |
srange |
Optional numeric vector of length 2 giving the range of values of bandwidth to be searched. |
ns |
Optional integer giving the number of values of bandwidth to search. |
sigma |
Optional. Vector of values of the bandwidth to be searched.
Overrides the values of |
warn |
Logical. If |
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]
.
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
.
Author(s)
Ottmar Cronie ottmar@chalmers.se and Marie-Colette van Lieshout Marie-Colette.van.Lieshout@cwi.nl. Adapted for spatstat by Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner rolfturner@posteo.net and Ege Rubak rubak@math.aau.dk.
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
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))
}