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
.