| bw.scott {spatstat.explore} | R Documentation |
Scott's Rule for Bandwidth Selection for Kernel Density
Description
Use Scott's rule of thumb to determine the smoothing bandwidth for the kernel estimation of point process intensity.
Usage
bw.scott(X, isotropic=FALSE, d=NULL)
bw.scott.iso(X)
Arguments
X |
A point pattern (object of class |
isotropic |
Logical value indicating whether to compute a single
bandwidth for an isotropic Gaussian kernel ( |
d |
Advanced use only. An integer value that should be used in Scott's formula instead of the true number of spatial dimensions. |
Details
These functions select a bandwidth sigma
for the kernel estimator of point process intensity
computed by density.ppp
or other appropriate functions.
They can be applied to a point pattern
belonging to any class "ppp", "lpp", "pp3"
or "ppx".
The bandwidth \sigma is computed by the rule of thumb
of Scott (1992, page 152, equation 6.42).
The bandwidth is proportional to n^{-1/(d+4)}
where n is the number of points and d is the number of
spatial dimensions.
This rule is very fast to compute. It typically produces a larger bandwidth
than bw.diggle. It is useful for estimating
gradual trend.
If isotropic=FALSE (the default), bw.scott provides a
separate bandwidth for each coordinate axis, and the result of the
function is a vector, of length equal to the number of coordinates.
If isotropic=TRUE, a single bandwidth value is computed
and the result is a single numeric value.
bw.scott.iso(X) is equivalent to
bw.scott(X, isotropic=TRUE).
The default value of d is as follows:
| class | dimension |
"ppp" | 2 |
"lpp" | 1 |
"pp3" | 3 |
"ppx" | number of spatial coordinates |
The use of d=1 for point patterns on a linear network
(class "lpp") was proposed by McSwiggan et al (2016)
and Rakshit et al (2019).
Value
A numerical value giving the selected bandwidth, or a numerical vector giving the selected bandwidths for each coordinate.
Author(s)
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner rolfturner@posteo.net and Ege Rubak rubak@math.aau.dk.
References
Scott, D.W. (1992) Multivariate Density Estimation. Theory, Practice and Visualization. New York: Wiley.
See Also
density.ppp,
bw.diggle,
bw.ppl,
bw.CvL,
bw.frac.
Examples
hickory <- split(lansing)[["hickory"]]
b <- bw.scott(hickory)
b
if(interactive()) {
plot(density(hickory, b))
}
bw.scott.iso(hickory)
bw.scott(osteo$pts[[1]])