Computes an adaptive estimate of the intensity function of a point pattern on a linear network, using the Dirichlet-Voronoi tessellation on the network.
Point pattern on a linear network (object of class
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
Number of independent repetitions of the randomised procedure.
Logical value indicating whether to print progress reports.
This function is an alternative to
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
for the class
"lpp" of point patterns on a linear network.
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
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.
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.
f is strictly between 0 and 1,
the smoothed Voronoi estimate (Moradi et al, 2019) is computed.
X is randomly
thinned by deleting or retaining each point independently, with
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
This procedure is repeated
nrep times and the results are
averaged to obtain the smoothed Voronoi estimate.
f can be chosen automatically by bandwidth
Pixel image on a linear network (object of class
and Mehdi Moradi.
Moradi, M., Cronie, 0., Rubak, E., Lachieze-Rey, R., Mateu, J. and Baddeley, A. (2019) Resample-smoothing of Voronoi intensity estimators. Statistics and Computing, in press.
lineardirichlet computes the Dirichlet-Voronoi
tessellation on a network.
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