| bw.ppl {spatstat} | R Documentation |
Uses likelihood cross-validation to select a smoothing bandwidth for the kernel estimation of point process intensity.
bw.ppl(X, ..., srange=NULL, ns=16)
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. |
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 maximise the point process likelihood cross-validation criterion
LCV(sigma) = sum[i] log(lambda[-i](x[i])) - integral[W] lambda(u) du
where the sum is taken over all the data points x[i], where lambda[-i](x_i) is the leave-one-out kernel-smoothing estimate of the intensity at x[i] with smoothing bandwidth sigma, and lambda(u) is the kernel-smoothing estimate of the intensity at a spatial location u with smoothing bandwidth sigma. See Loader(1999, Section 5.3).
The value of LCV(sigma) is computed
directly, using density.ppp,
for ns different values of sigma
between srange[1] and srange[2].
The result is a numerical value giving the selected bandwidth.
The result also belongs to the class "bw.optim"
which can be plotted to show the (rescaled) mean-square error
as a function of sigma.
A numerical value giving the selected bandwidth.
The result also belongs to the class "bw.optim"
which can be plotted.
Adrian Baddeley Adrian.Baddeley@uwa.edu.au http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner r.turner@auckland.ac.nz
Loader, C. (1999) Local Regression and Likelihood. Springer, New York.
density.ppp,
bw.diggle,
bw.scott
b <- bw.ppl(redwood)
plot(b, main="Likelihood cross validation for redwoods")
plot(density(redwood, b))