bw.ppl | 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, 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 \sigma
is chosen to
maximise the point process likelihood cross-validation criterion
\mbox{LCV}(\sigma) =
\sum_i \log\hat\lambda_{-i}(x_i) - \int_W \hat\lambda(u) \, {\rm d}u
where the sum is taken over all the data points x_i
,
where \hat\lambda_{-i}(x_i)
is the
leave-one-out kernel-smoothing estimate of the intensity at
x_i
with smoothing bandwidth \sigma
,
and \hat\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 \mbox{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
.
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.
.
Loader, C. (1999) Local Regression and Likelihood. Springer, New York.
density.ppp
,
bw.diggle
,
bw.scott
,
bw.CvL
,
bw.frac
.
if(interactive()) {
b <- bw.ppl(redwood)
plot(b, main="Likelihood cross validation for redwoods")
plot(density(redwood, b))
}
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