lohboot(X,
fun=c("pcf", "Kest", "Lest", "pcfinhom", "Kinhom", "Linhom"),
..., nsim=200, confidence=0.95, global=FALSE, type=7)"ppp")."pcf", "Kest", "Lest",
"pcfinhom", "Kinhom" or "Linhom".
Alternatively, tFALSE (the default), pointwise confidence intervals
are constructed. If TRUE, a global (simultaneous) confidence band is
constructed.quantile
controlling the way the quantiles are calculated."fv")
containing columns giving the estimate of the summary function,
the upper and lower limits of the bootstrap confidence interval,
and the theoretical value of the summary function for a Poisson process.fun using the bootstrap method of Loh (2008). If fun="pcf", for example, the algorithm computes a pointwise
(100 * confidence)% confidence interval for the true value of
the pair correlation function for the point process,
normally estimated by pcf.
It starts by computing the array of
local pair correlation functions,
localpcf, of the data pattern X.
This array consists of the contributions to the estimate of the
pair correlation function from each
data point. Then these contributions are resampled nsim times
with replacement; from each resampled dataset the total contribution
is computed, yielding nsim random pair correlation functions.
The pointwise alpha/2 and 1 - alpha/2 quantiles of
these functions are computed, where alpha = 1 - confidence.
The average of the local functions is also computed as an estimate
of the pair correlation function.
To control the estimation algorithm, use the
arguments ..., which are passed to the local version
of the summary function, as shown below:
pcf localpcf
Kest localK
Lest localK
pcfinhom localpcfinhom
Kinhom localKinhom
Linhom localKinhom
}
For fun="Lest", the calculations are first performed
as if fun="Kest", and then the square-root transformation is
applied to obtain the $L$-function.
Note that the confidence bands computed by
lohboot(fun="pcf") may not contain the estimate of the
pair correlation function computed by pcf,
because of differences between the algorithm parameters
(such as the choice of edge correction)
in localpcf and pcf.
If you are using lohboot, the
appropriate point estimate of the pair correlation itself is
the pointwise mean of the local estimates, which is provided
in the result of lohboot and is shown in the default plot.
If the confidence bands seem unbelievably narrow,
this may occur because the point pattern has a hard core
(the true pair correlation function is zero for certain values of
distance) or because of an optical illusion when the
function is steeply sloping (remember the width of the confidence
bands should be measured vertically).
An alternative to lohboot is varblock.
Kest,
pcf,
Kinhom,
pcfinhom,
localK,
localpcf,
localKinhom,
localpcfinhom. See varblock for an alternative bootstrap technique.
p <- lohboot(simdat, stoyan=0.5)
plot(p)Run the code above in your browser using DataLab