Intensity Estimate of Point Pattern on Linear Network Using Voronoi-Dirichlet Tessellation
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 class 'lpp' densityVoronoi(X, f = 1, ..., nrep = 1, verbose = TRUE)
X |
Point pattern on a linear network (object of class |
f |
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 |
nrep |
Number of independent repetitions of the randomised procedure. |
verbose |
Logical value indicating whether to print progress reports. |
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.
Pixel image on a linear network (object of class "linim").
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk 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.
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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