Scott's Rule for Bandwidth Selection for Kernel Density
Use Scott's rule of thumb to determine the smoothing bandwidth for the kernel estimation of point process intensity.
bw.scott(X, isotropic=FALSE, d=NULL) bw.scott.iso(X)
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. |
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 σ 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).
A numerical value giving the selected bandwidth, or a numerical vector giving the selected bandwidths for each coordinate.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.
Scott, D.W. (1992) Multivariate Density Estimation. Theory, Practice and Visualization. New York: Wiley.
hickory <- split(lansing)[["hickory"]]
b <- bw.scott(hickory)
b
if(interactive()) {
plot(density(hickory, b))
}
bw.scott.iso(hickory)
bw.scott(osteo$pts[[1]])Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.