bw.pcf  R Documentation 
Uses composite likelihood or generalized least squares crossvalidation to select a smoothing bandwidth for the kernel estimation of pair correlation function.
bw.pcf(X, rmax=NULL, lambda=NULL, divisor="r", kernel="epanechnikov", nr=10000, bias.correct=TRUE, cv.method=c("compLik", "leastSQ"), simple=TRUE, srange=NULL, ..., verbose=FALSE, warn=TRUE)
X 
A point pattern (object of class 
rmax 
Numeric. Maximum value of the spatial lag distance r for which g(r) should be evaluated. 
lambda 
Optional.
Values of the estimated intensity function.
A vector giving the intensity values
at the points of the pattern 
divisor 
Choice of divisor in the estimation formula:
either 
kernel 
Choice of smoothing kernel, passed to 
nr 
Integer. Number of subintervals for discretization of [0, rmax] to use in computing numerical integrals. 
bias.correct 
Logical. Whether to use bias corrected version of the kernel estimate. See Details. 
cv.method 
Choice of cross validation method: either

simple 
Logical. Whether to use simple removal of spatial lag distances. See Details. 
srange 
Optional. Numeric vector of length 2 giving the range of bandwidth values that should be searched to find the optimum bandwidth. 
... 
Other arguments, passed to 
verbose 
Logical value indicating whether to print progress reports during the optimization procedure. 
warn 
Logical. If 
This function selects an appropriate bandwidth bw
for the kernel estimator of the pair correlation function
of a point process intensity computed by pcf.ppp
(homogeneous case) or pcfinhom
(inhomogeneous case).
With cv.method="leastSQ"
, the bandwidth
h is chosen to minimise an unbiased
estimate of the integrated meansquare error criterion
M(h) defined in equation (4) in Guan (2007a).
The code implements the fast algorithm of Jalilian and Waagepetersen
(2018).
With cv.method="compLik"
, the bandwidth
h is chosen to maximise a likelihood
crossvalidation criterion CV(h) defined in
equation (6) of Guan (2007b).
M(b) = \int_{0}^{rmax} \hat{g}^2(r;b) r dr  ∑_{u,v}
The result is a numerical value giving the selected bandwidth.
A numerical value giving the selected bandwidth.
The result also belongs to the class "bw.optim"
which can be plotted.
The bandwidth bw
returned by bw.pcf
is the standard deviation of the smoothing kernel,
following the standard convention in R.
As mentioned in the documentation for
density.default
and pcf.ppp
,
this differs from other definitions of bandwidth that can be
found in the literature. The scale parameter
h
, which is called the bandwidth in some literature,
is defined differently.
For example for the Epanechnikov kernel, h
is the halfwidth
of the kernel, and bw=h/sqrt(5)
.
Rasmus Waagepetersen and Abdollah Jalilian. Adapted for spatstat by \spatstatAuthors.
Guan, Y. (2007a). A composite likelihood crossvalidation approach in selecting bandwidth for the estimation of the pair correlation function. Scandinavian Journal of Statistics, 34(2), 336–346.
Guan, Y. (2007b). A leastsquares crossvalidation bandwidth selection approach in pair correlation function estimations. Statistics & Probability Letters, 77(18), 1722–1729.
Jalilian, A. and Waagepetersen, R. (2018) Fast bandwidth selection for estimation of the pair correlation function. Journal of Statistical Computation and Simulation, 88(10), 2001–2011. https://www.tandfonline.com/doi/full/10.1080/00949655.2018.1428606
pcf.ppp
,
pcfinhom
b < bw.pcf(redwood) plot(pcf(redwood, bw=b))
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