Computes an adaptive estimate of the intensity function of a point pattern on a linear network, using the Dirichlet-Voronoi tessellation on the network.
# S3 method for lpp
densityVoronoi(X, f = 1, ..., nrep = 1, verbose = TRUE)Pixel image on a linear network (object of class "linim").
Point pattern on a linear network (object of class "lpp").
Fraction (between 0 and 1 inclusive) of the data points that will be used to build a tessellation for the intensity estimate.
Arguments passed to linim determining the
pixel resolution of the result.
Number of independent repetitions of the randomised procedure.
Logical value indicating whether to print progress reports.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner rolfturner@posteo.net and Ege Rubak rubak@math.aau.dk and Mehdi Moradi m2.moradi@yahoo.com.
This function is an alternative to density.lpp. It
computes an estimate of the intensity function of a point pattern
dataset on a linear network.
The result is a pixel image on the network, giving the estimated intensity.
This function is a method for the generic densityVoronoi
for the class "lpp" of point patterns on a linear network.
If f=1 (the default), the Voronoi estimate (Barr and Schoenberg, 2010)
is computed: the point pattern X is used to construct
a Voronoi/Dirichlet tessellation on the network
(see lineardirichlet);
the lengths of the Dirichlet tiles are computed; the estimated intensity
in each tile is the reciprocal of the tile length.
The result is a pixel image
of intensity estimates which are constant on each tile of the tessellation.
If f=0, the intensity estimate at every location is
equal to the average intensity (number of points divided by
network length). The result is a pixel image
of intensity estimates which are constant.
If f is strictly between 0 and 1,
the smoothed Voronoi estimate (Moradi et al, 2019) is computed.
The dataset X is randomly
thinned by deleting or retaining each point independently, with
probability f of retaining a point.
The thinned pattern
is used to construct a Dirichlet tessellation and form the
Voronoi estimate, which is then
adjusted by a factor 1/f.
This procedure is repeated nrep times and the results are
averaged to obtain the smoothed Voronoi estimate.
The value f can be chosen automatically by bandwidth
selection using bw.voronoi.
Moradi, M., Cronie, 0., Rubak, E., Lachieze-Rey, R., Mateu, J. and Baddeley, A. (2019) Resample-smoothing of Voronoi intensity estimators. Statistics and Computing 29 (5) 995--1010.
densityVoronoi is the generic, with a method for
class "ppp".
lineardirichlet computes the Dirichlet-Voronoi
tessellation on a network.
bw.voronoi performs bandwidth selection of the fraction f.
See also density.lpp.
nr <- if(interactive()) 100 else 3
plot(densityVoronoi(spiders, 0.1, nrep=nr))
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