Likelihood Cross Validation Bandwidth Selection for Kernel Density
Uses likelihood cross-validation to select a smoothing bandwidth for the kernel estimation of point process intensity.
bw.ppl(X, ..., srange=NULL, ns=16, sigma=NULL, weights=NULL,
shortcut=FALSE, warn=TRUE)X |
A point pattern (object of class |
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 |
weights |
Optional. Numeric vector of weights for the points of |
... |
Additional arguments passed to
|
shortcut |
Logical value indicating whether to speed up the calculation by omitting the integral term in the cross-validation criterion. |
warn |
Logical. If |
This function selects an appropriate bandwidth sigma
for the kernel estimator of point process intensity
computed by density.ppp.
The bandwidth σ is chosen to maximise the point process likelihood cross-validation criterion
LCV(σ) = sum[i] log(λ[-i](x[i])) - integral[W] λ(u) du
where the sum is taken over all the data points x[i], where λ[-i](x_i) is the leave-one-out kernel-smoothing estimate of the intensity at x[i] with smoothing bandwidth σ, and λ(u) is the kernel-smoothing estimate of the intensity at a spatial location u with smoothing bandwidth σ. See Loader(1999, Section 5.3).
The value of LCV(σ) is computed
directly, using density.ppp,
for ns different values of σ
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.
If shortcut=TRUE, the computation is accelerated by
omitting the integral term in the equation above. This is valid
because the integral is approximately constant.
A numerical value giving the selected bandwidth.
The result also belongs to the class "bw.optim"
which can be plotted.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.
Loader, C. (1999) Local Regression and Likelihood. Springer, New York.
if(interactive()) {
b <- bw.ppl(redwood)
plot(b, main="Likelihood cross validation for redwoods")
plot(density(redwood, b))
}Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.